Pub Date : 2025-12-24DOI: 10.1016/j.cam.2025.117263
Haneche Nabil , Hamaizia Tayeb
Fractional-order dynamic systems provide more realistic results than their ordinary counterparts due to the memory effect. This paper constructs a new hyperchaotic map using the Caputo fractional operator. A discrete dynamic system is required to describe more complex dynamical behaviors, such as chaos and hyperchaos, in the model. The exhibition of bifurcations by the fractional-order map has been investigated. Multiple positive Lyapunov exponents indicate that complex hyperchaotic dynamics have been exhibited when the fractional order or control parameters are varied. Also, the spectral entropy method (SE) is employed to measure accurately the fractional-order map’s level of complexity. It is shown that the fractional-order map has a high level of complexity compared to other discrete maps. Based on the chaotic sequences that were generated by this fractional-order map, a secure color image encryption algorithm is proposed. The proposed algorithm has superior encryption performance and high security. Experimental results and performance analysis show that this algorithm is accurate and secure for encrypting images, as it can stand up to different brute-force attacks.
{"title":"Dynamical analysis of a novel fractional-order hyperchaotic map and its application for fast color image encryption","authors":"Haneche Nabil , Hamaizia Tayeb","doi":"10.1016/j.cam.2025.117263","DOIUrl":"10.1016/j.cam.2025.117263","url":null,"abstract":"<div><div>Fractional-order dynamic systems provide more realistic results than their ordinary counterparts due to the memory effect. This paper constructs a new hyperchaotic map using the Caputo fractional operator. A discrete dynamic system is required to describe more complex dynamical behaviors, such as chaos and hyperchaos, in the model. The exhibition of bifurcations by the fractional-order map has been investigated. Multiple positive Lyapunov exponents indicate that complex hyperchaotic dynamics have been exhibited when the fractional order or control parameters are varied. Also, the spectral entropy method (SE) is employed to measure accurately the fractional-order map’s level of complexity. It is shown that the fractional-order map has a high level of complexity compared to other discrete maps. Based on the chaotic sequences that were generated by this fractional-order map, a secure color image encryption algorithm is proposed. The proposed algorithm has superior encryption performance and high security. Experimental results and performance analysis show that this algorithm is accurate and secure for encrypting images, as it can stand up to different brute-force attacks.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"481 ","pages":"Article 117263"},"PeriodicalIF":2.6,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-24DOI: 10.1016/j.cam.2025.117283
Liang Chen, Qiuqi Li, Hongyu Yang
This paper presents a non-intrusive model order reduction method based on nonlinear optimization for steady parameterized Stokes problems. To achieve this, we employ a weighted loss function to balance the velocity and pressure outputs to obtain a non-intrusive, data-driven algorithm utilizing only output samples. Moreover, we derive the gradients of the objective function with respect to the reduced-order matrices by resorting to the parameter-separable forms of reduced-model quantities. To enhance computational efficiency, our framework employs a two-stage offline-online decomposition. In the offline stage, we leverage gradient information to develop an optimization algorithm that computes optimal approximations for reduced-order matrices. In the online stage, the outputs can be quickly estimated for new parameter values using the reduced-order model obtained from the offline phase. Finally, we present numerical experiments to validate the effectiveness of this method, especially to demonstrate its capability to produce highly accurate approximation results.
{"title":"A non-intrusive model order reduction method based on nonlinear optimization for parameterized Stokes problems","authors":"Liang Chen, Qiuqi Li, Hongyu Yang","doi":"10.1016/j.cam.2025.117283","DOIUrl":"10.1016/j.cam.2025.117283","url":null,"abstract":"<div><div>This paper presents a non-intrusive model order reduction method based on nonlinear optimization for steady parameterized Stokes problems. To achieve this, we employ a weighted loss function to balance the velocity and pressure outputs to obtain a non-intrusive, data-driven algorithm utilizing only output samples. Moreover, we derive the gradients of the objective function with respect to the reduced-order matrices by resorting to the parameter-separable forms of reduced-model quantities. To enhance computational efficiency, our framework employs a two-stage offline-online decomposition. In the offline stage, we leverage gradient information to develop an optimization algorithm that computes optimal approximations for reduced-order matrices. In the online stage, the outputs can be quickly estimated for new parameter values using the reduced-order model obtained from the offline phase. Finally, we present numerical experiments to validate the effectiveness of this method, especially to demonstrate its capability to produce highly accurate approximation results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117283"},"PeriodicalIF":2.6,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-24DOI: 10.1016/j.cam.2025.117269
Leonidas Gkimisis , Süleyman Yıldız , Thomas Richter , Peter Benner
In this work, we investigate the data-driven inference of a discrete-time dynamical system via a sparse Full-Order Model (sFOM). We first formulate the involved Least Squares (LS) problem and discuss the need for regularization, indicating a connection between the typically employed l2 regularization and the stability of the inferred discrete-time sFOM. We then provide theoretical insights considering the consistency and stability properties of the inferred numerical schemes that form the sFOM and exemplify them via illustrative, 1D test cases of linear diffusion and linear advection. For linear advection, we analytically derive a “sampling CFL” condition, which dictates a bound for the ratio of spatial and temporal discretization steps in the training data that ensures stability of the inferred sFOM. Finally, we investigate the sFOM inference for two nonlinear problems, namely a 2D Burgers’ test case and the incompressible flow in an oscillating lid-driven cavity, and draw connections between the theoretical findings and the properties of the inferred, nonlinear sFOMs.
Novelty statement: sparse FOM inference for dynamical systems in discrete time. Theoretical insights on the analytical solution of the sparse FOM least-squares problem. Established connection between the stability of sparse FOM and the l2 regularization of the least-squares problem.
{"title":"A CFL-type condition and theoretical insights for discrete-time sparse full-order model inference","authors":"Leonidas Gkimisis , Süleyman Yıldız , Thomas Richter , Peter Benner","doi":"10.1016/j.cam.2025.117269","DOIUrl":"10.1016/j.cam.2025.117269","url":null,"abstract":"<div><div>In this work, we investigate the data-driven inference of a discrete-time dynamical system via a sparse Full-Order Model (sFOM). We first formulate the involved Least Squares (LS) problem and discuss the need for regularization, indicating a connection between the typically employed <em>l</em><sub>2</sub> regularization and the stability of the inferred discrete-time sFOM. We then provide theoretical insights considering the consistency and stability properties of the inferred numerical schemes that form the sFOM and exemplify them via illustrative, 1D test cases of linear diffusion and linear advection. For linear advection, we analytically derive a “sampling CFL” condition, which dictates a bound for the ratio of spatial and temporal discretization steps in the training data that ensures stability of the inferred sFOM. Finally, we investigate the sFOM inference for two nonlinear problems, namely a 2D Burgers’ test case and the incompressible flow in an oscillating lid-driven cavity, and draw connections between the theoretical findings and the properties of the inferred, nonlinear sFOMs.</div><div><strong>Novelty statement:</strong> sparse FOM inference for dynamical systems in discrete time. Theoretical insights on the analytical solution of the sparse FOM least-squares problem. Established connection between the stability of sparse FOM and the <em>l</em><sub>2</sub> regularization of the least-squares problem.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117269"},"PeriodicalIF":2.6,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-24DOI: 10.1016/j.cam.2025.117255
Longze Tan, Jingrun Chen
We study large-scale, ill-conditioned, and overdetermined least squares problems arising from the discretization of partial differential equations (PDEs), especially those induced by the random feature method (RFM). To address these challenges, our methods consist of three main components: (1) a count sketch technique is used to sketch the original matrix to a smaller matrix; (2) a QR factorization or a singular value decomposition is employed for the smaller matrix to obtain the preconditioner, which is multiplied to the original matrix from the right-hand side; (3) least squares iterative solvers are employed to solve the preconditioned least squares system. This leads to two high-precision randomized preconditioned methods, namely the CSQRP-LSQR and CSSVDP-LSQR methods, which explicitly construct the preconditioned matrix and thereby avoid the numerical instabilities associated with the implicit preconditioning used in methods such as Blendenpik and LSRN. Under mild assumptions, we show that the condition number of the preconditioned system is independent of that of the original matrix and also establish error estimates for the CSQRP-LSQR method. Extensive numerical experiments on two- and three-dimensional PDE problems demonstrate that the proposed methods consistently achieve superior stability, higher accuracy, and improved computational efficiency compared to LSRN, QR-based solvers, and state-of-the-art sparse direct solvers. In particular, the CSSVDP-LSQR method remains robust for large-scale ill-conditioned least squares problems with infinite condition numbers or rank deficiencies, significantly reducing solution errors while maintaining competitive runtime performance.
{"title":"High-precision randomized preconditioned iterative methods for the random feature method","authors":"Longze Tan, Jingrun Chen","doi":"10.1016/j.cam.2025.117255","DOIUrl":"10.1016/j.cam.2025.117255","url":null,"abstract":"<div><div>We study large-scale, ill-conditioned, and overdetermined least squares problems arising from the discretization of partial differential equations (PDEs), especially those induced by the random feature method (RFM). To address these challenges, our methods consist of three main components: (1) a count sketch technique is used to sketch the original matrix to a smaller matrix; (2) a QR factorization or a singular value decomposition is employed for the smaller matrix to obtain the preconditioner, which is multiplied to the original matrix from the right-hand side; (3) least squares iterative solvers are employed to solve the preconditioned least squares system. This leads to two high-precision randomized preconditioned methods, namely the CSQRP-LSQR and CSSVDP-LSQR methods, which explicitly construct the preconditioned matrix and thereby avoid the numerical instabilities associated with the implicit preconditioning used in methods such as Blendenpik and LSRN. Under mild assumptions, we show that the condition number of the preconditioned system is independent of that of the original matrix and also establish error estimates for the CSQRP-LSQR method. Extensive numerical experiments on two- and three-dimensional PDE problems demonstrate that the proposed methods consistently achieve superior stability, higher accuracy, and improved computational efficiency compared to LSRN, QR-based solvers, and state-of-the-art sparse direct solvers. In particular, the CSSVDP-LSQR method remains robust for large-scale ill-conditioned least squares problems with infinite condition numbers or rank deficiencies, significantly reducing solution errors while maintaining competitive runtime performance.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"481 ","pages":"Article 117255"},"PeriodicalIF":2.6,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-24DOI: 10.1016/j.cam.2025.117271
Mohsen Alshahrani , Buzheng Shan
In this work, we propose multicontinuum splitting schemes for the wave equation with a high-contrast coefficient, extending our previous research on multiscale flow problems. The proposed approach consists of two main parts: decomposing the solution space into distinct components, and designing tailored time discretization schemes to enhance computational efficiency. To achieve the decomposition, we employ a multicontinuum homogenization method to introduce physically meaningful macroscopic variables and to separate fast and slow dynamics, effectively isolating contrast effects in high-contrast cases. This decomposition enables the design of schemes where the fast-dynamics (contrast-dependent) component is treated implicitly, while the slow-dynamics (contrast-independent) component is handled explicitly. The idea of discrete energy conservation is applied to derive the stability conditions, which are contrast-independent with appropriately chosen continua. We further discuss strategies for optimizing the space decomposition. These include a Rayleigh quotient problem involving tensors, and an alternative generalized eigenvalue decomposition to reduce computational effort. Finally, various numerical examples are presented to validate the accuracy and stability of our proposed method.
{"title":"Multicontinuum splitting schemes for multiscale wave problems","authors":"Mohsen Alshahrani , Buzheng Shan","doi":"10.1016/j.cam.2025.117271","DOIUrl":"10.1016/j.cam.2025.117271","url":null,"abstract":"<div><div>In this work, we propose multicontinuum splitting schemes for the wave equation with a high-contrast coefficient, extending our previous research on multiscale flow problems. The proposed approach consists of two main parts: decomposing the solution space into distinct components, and designing tailored time discretization schemes to enhance computational efficiency. To achieve the decomposition, we employ a multicontinuum homogenization method to introduce physically meaningful macroscopic variables and to separate fast and slow dynamics, effectively isolating contrast effects in high-contrast cases. This decomposition enables the design of schemes where the fast-dynamics (contrast-dependent) component is treated implicitly, while the slow-dynamics (contrast-independent) component is handled explicitly. The idea of discrete energy conservation is applied to derive the stability conditions, which are contrast-independent with appropriately chosen continua. We further discuss strategies for optimizing the space decomposition. These include a Rayleigh quotient problem involving tensors, and an alternative generalized eigenvalue decomposition to reduce computational effort. Finally, various numerical examples are presented to validate the accuracy and stability of our proposed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"481 ","pages":"Article 117271"},"PeriodicalIF":2.6,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-23DOI: 10.1016/j.cam.2025.117282
Hao Wang, Yaoyao Chen
In this paper, we propose, analyze, and numerically validate a unconditionally energy-stable invariant energy quadratization (IEQ) adaptive finite element (AFE) method for the Allen–Cahn equation. The adaptive method is based on a linear and second-order scheme, for which the intermediate function introduced by the IEQ approach positioned in a combination of the continuous function and finite element spaces resulting in a cost-effective computation and ensuring unconditional energy decay in the finite element space introduced by Chen et al. [10]. An unconditionally energy stable discrete law for the modified energy is established for the fully discrete scheme. A posteriori error estimation based on the superconvergent patch recovery is constructed as the spatial error indicator, and the time derivative of the energy is proposed as the temporal error estimator. Based on the proposed error estimators, a time-space adaptive algorithm is designed for numerically approximating the Allen–Cahn equation. Several numerical experiments are presented to validate the reliability and efficiency of the proposed IEQ-AFE method and the corresponding adaptive algorithm. The extension of the proposed adaptive method to the Cahn–Hilliard equation is also discussed.
{"title":"Second order unconditional energy stable invariant energy quadratization adaptive finite element method for gradient flow models","authors":"Hao Wang, Yaoyao Chen","doi":"10.1016/j.cam.2025.117282","DOIUrl":"10.1016/j.cam.2025.117282","url":null,"abstract":"<div><div>In this paper, we propose, analyze, and numerically validate a unconditionally energy-stable invariant energy quadratization (IEQ) adaptive finite element (AFE) method for the Allen–Cahn equation. The adaptive method is based on a linear and second-order scheme, for which the intermediate function introduced by the IEQ approach positioned in a combination of the continuous function and finite element spaces resulting in a cost-effective computation and ensuring unconditional energy decay in the finite element space introduced by Chen et al. [10]. An unconditionally energy stable discrete law for the modified energy is established for the fully discrete scheme. A posteriori error estimation based on the superconvergent patch recovery is constructed as the spatial error indicator, and the time derivative of the energy is proposed as the temporal error estimator. Based on the proposed error estimators, a time-space adaptive algorithm is designed for numerically approximating the Allen–Cahn equation. Several numerical experiments are presented to validate the reliability and efficiency of the proposed IEQ-AFE method and the corresponding adaptive algorithm. The extension of the proposed adaptive method to the Cahn–Hilliard equation is also discussed.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"481 ","pages":"Article 117282"},"PeriodicalIF":2.6,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-23DOI: 10.1016/j.cam.2025.117278
Xiaojuan Wang , Xiaoping Xie , Shiquan Zhang
In this paper, we develop and analyze a class of linearized fully discrete weak Galerkin (WG) finite element methods for the unsteady Brinkman-Forchheimer model. For spatial discretization, the WG methods utilize the piecewise polynomials of degrees m (m ≥ 1) and to approximate the velocity and the pressure within the interior of elements, respectively. Additionally, piecewise polynomials of degree m are employed for their corresponding numerical traces on the element interfaces. For temporal discretization, a linearized backward Euler difference scheme is formulated, where semi-implicit techniques are adopted to deal with the nonlinear terms. The proposed methods ensure that the velocity approximation is globally divergence - free. The well-posedness and optimal error estimates, both in the energy norm and L2 norm, are rigorously derived. Numerical tests are conducted to validate the established theoretical results.
{"title":"Analysis of a class of globally divergence-free linearized fully discrete WG methods for unsteady Brinkman-Forchheimer equations","authors":"Xiaojuan Wang , Xiaoping Xie , Shiquan Zhang","doi":"10.1016/j.cam.2025.117278","DOIUrl":"10.1016/j.cam.2025.117278","url":null,"abstract":"<div><div>In this paper, we develop and analyze a class of linearized fully discrete weak Galerkin (WG) finite element methods for the unsteady Brinkman-Forchheimer model. For spatial discretization, the WG methods utilize the piecewise polynomials of degrees <em>m</em> (<em>m</em> ≥ 1) and <span><math><mrow><mi>m</mi><mo>−</mo><mn>1</mn></mrow></math></span> to approximate the velocity and the pressure within the interior of elements, respectively. Additionally, piecewise polynomials of degree <em>m</em> are employed for their corresponding numerical traces on the element interfaces. For temporal discretization, a linearized backward Euler difference scheme is formulated, where semi-implicit techniques are adopted to deal with the nonlinear terms. The proposed methods ensure that the velocity approximation is globally divergence - free. The well-posedness and optimal error estimates, both in the energy norm and <em>L</em><sup>2</sup> norm, are rigorously derived. Numerical tests are conducted to validate the established theoretical results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"481 ","pages":"Article 117278"},"PeriodicalIF":2.6,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-23DOI: 10.1016/j.cam.2025.117268
Xiao Chen , Yixin Luo , Jingrun Chen
In this paper, we propose a hybrid method that combines finite element method (FEM) and physics-informed neural network (PINN) for solving linear elliptic problems. This method contains three steps: (1) train a PINN and obtain an approximate solution uθ; (2) enrich the finite element space with uθ; (3) obtain the final solution by FEM in the enriched space. In the second step, the enriched space is constructed by addition or multiplication v · uθ, where v belongs to the standard finite element space. We conduct the convergence analysis for the proposed method. Compared to the standard FEM, the same convergence order is obtained and higher accuracy can be achieved when solution derivatives are well approximated in PINN. Numerical examples from one dimension to three dimensions verify these theoretical results, and show that in fine mesh resolutions, the proposed method has higher accuracy than finite element method with lower time cost.
{"title":"A PINN-enriched finite element method for linear elliptic problems","authors":"Xiao Chen , Yixin Luo , Jingrun Chen","doi":"10.1016/j.cam.2025.117268","DOIUrl":"10.1016/j.cam.2025.117268","url":null,"abstract":"<div><div>In this paper, we propose a hybrid method that combines finite element method (FEM) and physics-informed neural network (PINN) for solving linear elliptic problems. This method contains three steps: (1) train a PINN and obtain an approximate solution <em>u<sub>θ</sub></em>; (2) enrich the finite element space with <em>u<sub>θ</sub></em>; (3) obtain the final solution by FEM in the enriched space. In the second step, the enriched space is constructed by addition <span><math><mrow><mi>v</mi><mo>+</mo><msub><mi>u</mi><mi>θ</mi></msub></mrow></math></span> or multiplication <em>v</em> · <em>u<sub>θ</sub></em>, where <em>v</em> belongs to the standard finite element space. We conduct the convergence analysis for the proposed method. Compared to the standard FEM, the same convergence order is obtained and higher accuracy can be achieved when solution derivatives are well approximated in PINN. Numerical examples from one dimension to three dimensions verify these theoretical results, and show that in fine mesh resolutions, the proposed method has higher accuracy than finite element method with lower time cost.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"481 ","pages":"Article 117268"},"PeriodicalIF":2.6,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-22DOI: 10.1016/j.cam.2025.117280
Yun-Bo Yang , Yiru Chen
In this paper, we present a fully explicitly uncoupled variational multiscale (VMS) stabilization finite element method for solving the nonlinear fluid-fluid interaction model, which consists of Navier-Stokes equations coupled by some nonlinear interface. The presented method introduces the decoupled VMS treatments as post-processing steps at each time step, and thus can be easily implemented because the existing codes can be used. We prove the unconditional stability and derive the a priori error estimates. Ample numerical tests are also given to confirm the theoretical analysis and to demonstrate the efficiency of the new method.
{"title":"An explicitly decoupled variational multiscale method for a nonlinear fluid-fluid interaction model","authors":"Yun-Bo Yang , Yiru Chen","doi":"10.1016/j.cam.2025.117280","DOIUrl":"10.1016/j.cam.2025.117280","url":null,"abstract":"<div><div>In this paper, we present a fully explicitly uncoupled variational multiscale (VMS) stabilization finite element method for solving the nonlinear fluid-fluid interaction model, which consists of Navier-Stokes equations coupled by some nonlinear interface. The presented method introduces the decoupled VMS treatments as post-processing steps at each time step, and thus can be easily implemented because the existing codes can be used. We prove the unconditional stability and derive the a priori error estimates. Ample numerical tests are also given to confirm the theoretical analysis and to demonstrate the efficiency of the new method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"481 ","pages":"Article 117280"},"PeriodicalIF":2.6,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-22DOI: 10.1016/j.cam.2025.117274
Xiaoxin Wu
This paper presents a novel family of quadratic finite volume (QFV) schemes for solving anisotropic diffusion problems on triangular meshes. While retaining the primary mesh structure and quadratic trial spaces of conventional QFV methods, our approach introduces a significant innovation through the construction of dual meshes governed by three independent parameters (α, β, γ). The introduction of parameter γ enables independent control over boundary partitioning, expanding the family of admissible dual configurations beyond classical two-parameter constructions. This enhanced parameterization framework facilitates the development of L2-optimal QFV schemes with improved geometric flexibility. We establish rigorous theoretical foundations for the proposed methods, including a coercivity analysis under parameter-dependent stability conditions and optimal error estimates in both H1- and L2-norms. Notably, our framework reduces the minimum angle requirement for mesh elements by 0.03∘ compared to existing L2-optimal QFV schemes. Some numerical experiments are presented to demonstrate the theoretical error estimates.
{"title":"L2-Optimal quadratic finite volume schemes for anisotropic diffusion problems on triangular meshes via three-parameter dual mesh construction","authors":"Xiaoxin Wu","doi":"10.1016/j.cam.2025.117274","DOIUrl":"10.1016/j.cam.2025.117274","url":null,"abstract":"<div><div>This paper presents a novel family of quadratic finite volume (QFV) schemes for solving anisotropic diffusion problems on triangular meshes. While retaining the primary mesh structure and quadratic trial spaces of conventional QFV methods, our approach introduces a significant innovation through the construction of dual meshes governed by three independent parameters (<em>α, β, γ</em>). The introduction of parameter <em>γ</em> enables independent control over boundary partitioning, expanding the family of admissible dual configurations beyond classical two-parameter constructions. This enhanced parameterization framework facilitates the development of <em>L</em><sup>2</sup>-optimal QFV schemes with improved geometric flexibility. We establish rigorous theoretical foundations for the proposed methods, including a coercivity analysis under parameter-dependent stability conditions and optimal error estimates in both <em>H</em><sup>1</sup>- and <em>L</em><sup>2</sup>-norms. Notably, our framework reduces the minimum angle requirement for mesh elements by 0.03<sup>∘</sup> compared to existing <em>L</em><sup>2</sup>-optimal QFV schemes. Some numerical experiments are presented to demonstrate the theoretical error estimates.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"481 ","pages":"Article 117274"},"PeriodicalIF":2.6,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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