Pub Date : 2026-01-03DOI: 10.1016/j.cam.2026.117338
Davoud Mirzaei , Vahid Mohammadi
This paper presents a vector-valued moving least squares (MLS) approximation for reconstructing vector fields that are divergence-free or curl-free. The proposed method constructs analytically divergence-free or curl-free shape functions by applying appropriate differential operators to a stream (potential) function approximated using the MLS method. The procedure involves solving a sparse linear least squares problem, for which the Conjugate Gradient Least Squares (CGLS) algorithm is employed to reduce computational costs compared to the direct solvers. The approach relies solely on a set of scattered nodes in the computational domain and requires no background triangulation. We provide error bounds for the approximation and support the theoretical bounds with numerical experiments. Additionally, we demonstrate the application of the divergence-free MLS approximation to the numerical solution of Darcy’s flow equations.
{"title":"Divergence-free and curl-free moving least squares approximations","authors":"Davoud Mirzaei , Vahid Mohammadi","doi":"10.1016/j.cam.2026.117338","DOIUrl":"10.1016/j.cam.2026.117338","url":null,"abstract":"<div><div>This paper presents a vector-valued moving least squares (MLS) approximation for reconstructing vector fields that are divergence-free or curl-free. The proposed method constructs <em>analytically</em> divergence-free or curl-free shape functions by applying appropriate differential operators to a stream (potential) function approximated using the MLS method. The procedure involves solving a sparse linear least squares problem, for which the Conjugate Gradient Least Squares (CGLS) algorithm is employed to reduce computational costs compared to the direct solvers. The approach relies solely on a set of scattered nodes in the computational domain and requires no background triangulation. We provide error bounds for the approximation and support the theoretical bounds with numerical experiments. Additionally, we demonstrate the application of the divergence-free MLS approximation to the numerical solution of Darcy’s flow equations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117338"},"PeriodicalIF":2.6,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928216","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 : 2026-01-02DOI: 10.1016/j.cam.2025.117331
Hsueh-Chen Lee , Hyesuk Lee
This study presents an integrated approach that combines the Galerkin least-squares (GLS) finite element method with deep neural networks (DNNs) to efficiently simulate generalized Newtonian flows of power-law fluids in porous media. The GLS method is employed to solve the two-dimensional nonlinear Brinkman equations, incorporating stabilization terms to address finite element space incompatibility by treating velocity, pressure, and stress as independent variables. Picard linearization and weak formulation ensure numerical stability and convergence, with the method achieving theoretical convergence rates in the L2-norm using low-order basis functions. To improve computational efficiency, a surrogate model based on DNNs is developed and validated for accuracy. The DNN is trained on GLS-generated data with a train/validation/test protocol, early stopping, and L2 regularization, thus ensuring an efficient accelerator for parameter studies requiring multiple simulations. By combining the numerical accuracy of the GLS method with the computational efficiency of DNNs, this hybrid approach enables rapid and scalable simulations of linearized Brinkman flows. The methodology is applied to pore-scale flow problems, demonstrating the DNN’s capability to replicate GLS solutions with low residual errors and significantly reduced computational costs. This study highlights the synergy between finite element methods and machine learning, offering a scalable and efficient solution for modeling complex fluid dynamics in porous media.
{"title":"A Galerkin least-squares finite element method within deep neural networks for efficient simulation of generalized Newtonian flows in porous media","authors":"Hsueh-Chen Lee , Hyesuk Lee","doi":"10.1016/j.cam.2025.117331","DOIUrl":"10.1016/j.cam.2025.117331","url":null,"abstract":"<div><div>This study presents an integrated approach that combines the Galerkin least-squares (GLS) finite element method with deep neural networks (DNNs) to efficiently simulate generalized Newtonian flows of power-law fluids in porous media. The GLS method is employed to solve the two-dimensional nonlinear Brinkman equations, incorporating stabilization terms to address finite element space incompatibility by treating velocity, pressure, and stress as independent variables. Picard linearization and weak formulation ensure numerical stability and convergence, with the method achieving theoretical convergence rates in the <em>L</em><sup>2</sup>-norm using low-order basis functions. To improve computational efficiency, a surrogate model based on DNNs is developed and validated for accuracy. The DNN is trained on GLS-generated data with a train/validation/test protocol, early stopping, and <em>L</em><sup>2</sup> regularization, thus ensuring an efficient accelerator for parameter studies requiring multiple simulations. By combining the numerical accuracy of the GLS method with the computational efficiency of DNNs, this hybrid approach enables rapid and scalable simulations of linearized Brinkman flows. The methodology is applied to pore-scale flow problems, demonstrating the DNN’s capability to replicate GLS solutions with low residual errors and significantly reduced computational costs. This study highlights the synergy between finite element methods and machine learning, offering a scalable and efficient solution for modeling complex fluid dynamics in porous media.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117331"},"PeriodicalIF":2.6,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928217","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 : 2026-01-02DOI: 10.1016/j.cam.2025.117334
Yanhua Mei , Jintao Cui , Yi Zhang , Fuzheng Gao
In this paper, we study a C0 nonsymmetric interior penalty method for the displacement obstacle problem of Kirchhoff plates on two and three dimensional general polygonal/polyhedral domains. We derive the error in an H2-like energy norm that converges in O(hα), where α is the index of elliptic regularity. Numerical experiments are performed to illustrate the theoretical results.
{"title":"A C0 nonsymmetric interior penalty method for fourth order variational inequality","authors":"Yanhua Mei , Jintao Cui , Yi Zhang , Fuzheng Gao","doi":"10.1016/j.cam.2025.117334","DOIUrl":"10.1016/j.cam.2025.117334","url":null,"abstract":"<div><div>In this paper, we study a <em>C</em><sup>0</sup> nonsymmetric interior penalty method for the displacement obstacle problem of Kirchhoff plates on two and three dimensional general polygonal/polyhedral domains. We derive the error in an <em>H</em><sup>2</sup>-like energy norm that converges in <em>O</em>(<em>h<sup>α</sup></em>), where <em>α</em> is the index of elliptic regularity. Numerical experiments are performed to illustrate the theoretical results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117334"},"PeriodicalIF":2.6,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928215","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 : 2025-12-31DOI: 10.1016/j.cam.2025.117330
Wenyue Zheng, Liqun Zhou, Mou Zou
This paper investigates the global polynomial synchronization (GPS) problem of neutral-type Cohen-Grossberg neural networks (NTCGNNs) with proportional delays (PDs). First, a feedback controller is designed and a Lyapunov functional (LF) is constructed by introducing polynomial functions. We establish a delay-dependent GPS criterion. Second, building upon the feedback control framework, by introducing polynomial functions, we design an adaptive controller and construct a LF, resulting in a GPS criterion that does not require additional verification conditions. Introducing polynomial functions simultaneously in the controller and LF enables the determination of GPS without constraints, which is a key innovation of this paper. Finally, the theoretical results are validated through two numerical examples, and the synchronization control scheme is successfully applied to image encryption.
{"title":"Global polynomial synchronization of neutral-type Cohen-Grossberg neural networks with proportional delays and its application to image encryption","authors":"Wenyue Zheng, Liqun Zhou, Mou Zou","doi":"10.1016/j.cam.2025.117330","DOIUrl":"10.1016/j.cam.2025.117330","url":null,"abstract":"<div><div>This paper investigates the global polynomial synchronization (GPS) problem of neutral-type Cohen-Grossberg neural networks (NTCGNNs) with proportional delays (PDs). First, a feedback controller is designed and a Lyapunov functional (LF) is constructed by introducing polynomial functions. We establish a delay-dependent GPS criterion. Second, building upon the feedback control framework, by introducing polynomial functions, we design an adaptive controller and construct a LF, resulting in a GPS criterion that does not require additional verification conditions. Introducing polynomial functions simultaneously in the controller and LF enables the determination of GPS without constraints, which is a key innovation of this paper. Finally, the theoretical results are validated through two numerical examples, and the synchronization control scheme is successfully applied to image encryption.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117330"},"PeriodicalIF":2.6,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928218","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 : 2025-12-31DOI: 10.1016/j.cam.2025.117314
Xiaoyuan Xu , Chengjian Zhang
Overlapping Schwarz waveform relaxation (OSWR) methods are a class of highly effective numerical methods for solving evolution problems. Nevertheless, for the delay evolution problems, so far no superlinearly-convergent OSWR method has been presented. To make up for this deficiency, in the present paper, we suggest a parallel-implementable OSWR method for solving delay reaction-diffusion equations and prove that this method is superlinearly convergent. The provided numerical experiments further verify the superlinear convergence of the presented OSWR method and its comparability with the existing serial OSWR methods in computational efficiency.
{"title":"A parallel-implementable superlinearly-convergent OSWR method for delay-reaction-diffusion equations","authors":"Xiaoyuan Xu , Chengjian Zhang","doi":"10.1016/j.cam.2025.117314","DOIUrl":"10.1016/j.cam.2025.117314","url":null,"abstract":"<div><div>Overlapping Schwarz waveform relaxation (OSWR) methods are a class of highly effective numerical methods for solving evolution problems. Nevertheless, for the delay evolution problems, so far no superlinearly-convergent OSWR method has been presented. To make up for this deficiency, in the present paper, we suggest a parallel-implementable OSWR method for solving delay reaction-diffusion equations and prove that this method is superlinearly convergent. The provided numerical experiments further verify the superlinear convergence of the presented OSWR method and its comparability with the existing serial OSWR methods in computational efficiency.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117314"},"PeriodicalIF":2.6,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928202","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 : 2025-12-30DOI: 10.1016/j.cam.2025.117316
Laura Selicato , Flavia Esposito , Andersen Ang , Nicoletta Del Buono , Rafał Zdunek
The selection of penalty hyperparameters is a critical aspect in Nonnegative Matrix Factorization (NMF), since these values control the trade-off between reconstruction accuracy and adherence to desired constraints. In this work, we focus on an NMF problem involving the Itakura-Saito (IS) divergence, which is particularly effective for extracting low spectral density components from spectrograms of mixed signals, and benefits from the introduction of sparsity constraints. We propose a new algorithm called SHINBO, which introduces a bi-level optimization framework to automatically and adaptively tune the row-dependent penalty hyperparameters, enhancing the ability of IS-NMF to isolate sparse, periodic signals in noisy environments. Experimental results demonstrate that SHINBO achieves accurate spectral decompositions and demonstrates superior performance in both synthetic and real-world applications. In the latter case, SHINBO is particularly useful for noninvasive vibration-based fault detection in rolling bearings, where the desired signal components often reside in high-frequency subbands but are obscured by stronger, spectrally broader noise. By addressing the critical issue of hyperparameter selection, SHINBO improves the state-of-the-art in signal recovery for complex, noise-dominated environments.
{"title":"Sparse hyperparametric Itakura-Saito nonnegative matrix factorization via bi-level optimization","authors":"Laura Selicato , Flavia Esposito , Andersen Ang , Nicoletta Del Buono , Rafał Zdunek","doi":"10.1016/j.cam.2025.117316","DOIUrl":"10.1016/j.cam.2025.117316","url":null,"abstract":"<div><div>The selection of penalty hyperparameters is a critical aspect in Nonnegative Matrix Factorization (NMF), since these values control the trade-off between reconstruction accuracy and adherence to desired constraints. In this work, we focus on an NMF problem involving the Itakura-Saito (IS) divergence, which is particularly effective for extracting low spectral density components from spectrograms of mixed signals, and benefits from the introduction of sparsity constraints. We propose a new algorithm called SHINBO, which introduces a bi-level optimization framework to automatically and adaptively tune the row-dependent penalty hyperparameters, enhancing the ability of IS-NMF to isolate sparse, periodic signals in noisy environments. Experimental results demonstrate that SHINBO achieves accurate spectral decompositions and demonstrates superior performance in both synthetic and real-world applications. In the latter case, SHINBO is particularly useful for noninvasive vibration-based fault detection in rolling bearings, where the desired signal components often reside in high-frequency subbands but are obscured by stronger, spectrally broader noise. By addressing the critical issue of hyperparameter selection, SHINBO improves the state-of-the-art in signal recovery for complex, noise-dominated environments.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117316"},"PeriodicalIF":2.6,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928214","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 : 2025-12-30DOI: 10.1016/j.cam.2025.117317
Mariantonia Cotronei , Woula Themistoclakis , Marc Van Barel
This paper investigates the potential applications of a parametric family of polynomial wavelets that has been recently introduced starting from de la Vallée Poussin (VP) interpolation at Chebyshev nodes. Unlike classical wavelets, which are constructed on the real line, these VP wavelets are defined on a bounded interval, offering the advantage of handling boundaries naturally while maintaining computational efficiency. In addition, the structure of these wavelets enables the use of fast algorithms for decomposition and reconstruction. Furthermore, the flexibility offered by a free parameter allows a better control of localized singularities, such as edges in images. On the basis of previous theoretical foundations, we show the effectiveness of the VP wavelets for basic signal denoising and image compression, emphasizing their potential for more advanced signal and image processing tasks.
本文从Chebyshev节点的de la vall Poussin （VP）插值开始，研究了最近引入的参数多项式小波族的潜在应用。与在实线上构造的经典小波不同，这些VP小波是在有界区间上定义的，在保持计算效率的同时，提供了自然处理边界的优势。此外，这些小波的结构允许使用快速算法进行分解和重建。此外，自由参数提供的灵活性允许更好地控制局部奇点，例如图像中的边缘。在先前理论基础的基础上，我们展示了VP小波在基本信号去噪和图像压缩方面的有效性，强调了它们在更高级的信号和图像处理任务中的潜力。
{"title":"A parametric family of polynomial wavelets for signal and image processing","authors":"Mariantonia Cotronei , Woula Themistoclakis , Marc Van Barel","doi":"10.1016/j.cam.2025.117317","DOIUrl":"10.1016/j.cam.2025.117317","url":null,"abstract":"<div><div>This paper investigates the potential applications of a parametric family of polynomial wavelets that has been recently introduced starting from de la Vallée Poussin (VP) interpolation at Chebyshev nodes. Unlike classical wavelets, which are constructed on the real line, these VP wavelets are defined on a bounded interval, offering the advantage of handling boundaries naturally while maintaining computational efficiency. In addition, the structure of these wavelets enables the use of fast algorithms for decomposition and reconstruction. Furthermore, the flexibility offered by a free parameter allows a better control of localized singularities, such as edges in images. On the basis of previous theoretical foundations, we show the effectiveness of the VP wavelets for basic signal denoising and image compression, emphasizing their potential for more advanced signal and image processing tasks.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117317"},"PeriodicalIF":2.6,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928220","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 : 2025-12-30DOI: 10.1016/j.cam.2025.117324
Francesco Della Santa
This work introduces a method to compute descent directions common to two or more differentiable functions defined over a shared unconstrained domain. Building on this, an alternative Multiple-Gradient Descent procedure for Multi-Objective Optimization problems is proposed. The core of the approach consists of solving a relatively cheap Linear Programming (LP) problem, where the objective and constraints are constructed from the gradients of the functions involved. In particular, the LP formulation is designed such that, when a common descent direction does not exist, it still yields a direction that is perpendicular to all objectives’ gradients, if such a direction is available. Additionally, a tailored backtracking strategy is presented, enhancing the performance of Multiple-Gradient Descent methods, especially when paired with the proposed LP-based direction computation, by improving the exploration of the Pareto set and front. Theoretical analysis and experiments on standard benchmark problems are provided to evaluate the effectiveness of the proposed techniques.
{"title":"A linear programming framework and an improved backtracking strategy for multiple-gradient descent","authors":"Francesco Della Santa","doi":"10.1016/j.cam.2025.117324","DOIUrl":"10.1016/j.cam.2025.117324","url":null,"abstract":"<div><div>This work introduces a method to compute descent directions common to two or more differentiable functions defined over a shared unconstrained domain. Building on this, an alternative Multiple-Gradient Descent procedure for Multi-Objective Optimization problems is proposed. The core of the approach consists of solving a relatively cheap Linear Programming (LP) problem, where the objective and constraints are constructed from the gradients of the functions involved. In particular, the LP formulation is designed such that, when a common descent direction does not exist, it still yields a direction that is perpendicular to all objectives’ gradients, if such a direction is available. Additionally, a tailored backtracking strategy is presented, enhancing the performance of Multiple-Gradient Descent methods, especially when paired with the proposed LP-based direction computation, by improving the exploration of the Pareto set and front. Theoretical analysis and experiments on standard benchmark problems are provided to evaluate the effectiveness of the proposed techniques.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117324"},"PeriodicalIF":2.6,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928200","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 : 2025-12-30DOI: 10.1016/j.cam.2025.117329
Jin Wen, Meng-Yao Zhou
This paper investigates the problem of simultaneously determining the initial value and initial velocity for the fractional diffusion-wave equation with singular perturbation, through the supplementary measurement data at two fixed time points. The paper derives the uniqueness of the solution to inverse problem by using the analytical and asymptotic characteristics of the Mittag-Leffler function, provided that the distance of these two time points is sufficiently small. In light of the problem’s ill-posedness, we adopt a boundary collocation method to solve this inverse problem, and use the Tikhonov regularization method combined with the GCV strategy. To demonstrate the efficiency and accuracy of our proposed method, we present several numerical examples in one-dimensional and two-dimensional cases.
{"title":"A regularization strategy for the backward problem for the fractional diffusion-wave equation with singular perturbation","authors":"Jin Wen, Meng-Yao Zhou","doi":"10.1016/j.cam.2025.117329","DOIUrl":"10.1016/j.cam.2025.117329","url":null,"abstract":"<div><div>This paper investigates the problem of simultaneously determining the initial value and initial velocity for the fractional diffusion-wave equation with singular perturbation, through the supplementary measurement data at two fixed time points. The paper derives the uniqueness of the solution to inverse problem by using the analytical and asymptotic characteristics of the Mittag-Leffler function, provided that the distance of these two time points is sufficiently small. In light of the problem’s ill-posedness, we adopt a boundary collocation method to solve this inverse problem, and use the Tikhonov regularization method combined with the GCV strategy. To demonstrate the efficiency and accuracy of our proposed method, we present several numerical examples in one-dimensional and two-dimensional cases.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117329"},"PeriodicalIF":2.6,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928219","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 : 2025-12-29DOI: 10.1016/j.cam.2025.117326
Chunmei Wang , Shangyou Zhang
This paper introduces a novel weak Galerkin (WG) finite element method for the numerical solution of the Brinkman equations. The Brinkman model, which seamlessly integrates characteristics of both the Stokes and Darcy equations, is employed to describe fluid flow in multiphysics contexts, particularly within heterogeneous porous media exhibiting spatially variable permeability. The proposed WG method offers a unified and robust approach capable of accurately capturing both Stokes- and Darcy-dominated regimes. A discrete inf-sup condition is established, and optimal-order error estimates are rigorously proven for the WG finite element solutions. Furthermore, a series of numerical experiments is performed to corroborate the theoretical analysis, demonstrating the method’s accuracy and stability in addressing the complexities inherent in the Brinkman equations.
{"title":"Weak galerkin methods for the Brinkman equations","authors":"Chunmei Wang , Shangyou Zhang","doi":"10.1016/j.cam.2025.117326","DOIUrl":"10.1016/j.cam.2025.117326","url":null,"abstract":"<div><div>This paper introduces a novel weak Galerkin (WG) finite element method for the numerical solution of the Brinkman equations. The Brinkman model, which seamlessly integrates characteristics of both the Stokes and Darcy equations, is employed to describe fluid flow in multiphysics contexts, particularly within heterogeneous porous media exhibiting spatially variable permeability. The proposed WG method offers a unified and robust approach capable of accurately capturing both Stokes- and Darcy-dominated regimes. A discrete inf-sup condition is established, and optimal-order error estimates are rigorously proven for the WG finite element solutions. Furthermore, a series of numerical experiments is performed to corroborate the theoretical analysis, demonstrating the method’s accuracy and stability in addressing the complexities inherent in the Brinkman equations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117326"},"PeriodicalIF":2.6,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886045","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号