Pub Date : 2026-05-15Epub Date: 2026-03-03DOI: 10.1016/j.camwa.2026.02.019
Dongmei Duan , Fuzheng Gao , Xiaoming He , Yanping Lin
This paper carries out the optimal L2 error estimation for a fully discrete method, which was proposed in [J. Sci. Comput., 95(1):16, 2023] for the Cahn-Hilliard-MHD model with constant coefficients. Compared with the original scheme, we adopt weaker regularity requirement for the finite element space of the discrete phase field. To obtain the optimal convergence order, -superconvergence error estimates of Ritz projection and Ritz quasi-projection are employed. The H1 semi-norm and L2 norm terms of the phase-field system, arising from the norm pair, are estimated by two sets of test functions. Furthermore, the first-order differential operator induces a loss of convergence rate in the projection error terms. Hence Ritz quasi-projection and Stokes quasi-projection, incorporating the above terms, are adopted from [SIAM J. Numer. Anal.,61(3):1218-1245, 2023]. Additionally, operator transfer based on Green’s formula provides an alternative strategy. We also carry out numerical examples to validate the numerical scheme.
{"title":"Optimal L2 error estimates for a fully discrete method of the Cahn-Hilliard-MHD model","authors":"Dongmei Duan , Fuzheng Gao , Xiaoming He , Yanping Lin","doi":"10.1016/j.camwa.2026.02.019","DOIUrl":"10.1016/j.camwa.2026.02.019","url":null,"abstract":"<div><div>This paper carries out the optimal <em>L</em><sup>2</sup> error estimation for a fully discrete method, which was proposed in [J. Sci. Comput., 95(1):16, 2023] for the Cahn-Hilliard-MHD model with constant coefficients. Compared with the original scheme, we adopt weaker regularity requirement for the finite element space of the discrete phase field. To obtain the optimal convergence order, <span><math><msup><mi>H</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span>-superconvergence error estimates of Ritz projection and Ritz quasi-projection are employed. The <em>H</em><sup>1</sup> semi-norm and <em>L</em><sup>2</sup> norm terms of the phase-field system, arising from the <span><math><mrow><msup><mi>H</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mspace></mspace><mo>−</mo><mspace></mspace><msup><mi>H</mi><mn>1</mn></msup></mrow></math></span> norm pair, are estimated by two sets of test functions. Furthermore, the first-order differential operator induces a loss of convergence rate in the projection error terms. Hence Ritz quasi-projection and Stokes quasi-projection, incorporating the above terms, are adopted from [SIAM J. Numer. Anal.,61(3):1218-1245, 2023]. Additionally, operator transfer based on Green’s formula provides an alternative strategy. We also carry out numerical examples to validate the numerical scheme.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"210 ","pages":"Pages 43-59"},"PeriodicalIF":2.5,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147359875","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 : 2026-05-15Epub Date: 2026-03-05DOI: 10.1016/j.camwa.2026.02.020
Zhen Zhang, Xiaoxing Liu
Although arbitrary-order accuracy can be achieved in meshless particle methods by combining Taylor-series expansion with least-squares techniques, this approach incurs high computational costs due to the inversion of high-order matrices. In this study, we develop a novel meshless method called least-square finite volume particle (LSFVP) method for solving PDEs efficiently. The particles are modeled as squares in two-dimensional space. The integral form of the PDEs is discretized for each finite volume particle using the LSFVP framework. The original second-order derivative is conceptually transformed into a first-order derivative. The least square method is employed to estimate the flux across particle surfaces, while Gauss integration ensures the overall second-order accuracy in evaluating surface flux integrals. Several numerical examples are presented to validate the proposed LSFVP method.
{"title":"Least square finite volume particle method for solving PDEs","authors":"Zhen Zhang, Xiaoxing Liu","doi":"10.1016/j.camwa.2026.02.020","DOIUrl":"10.1016/j.camwa.2026.02.020","url":null,"abstract":"<div><div>Although arbitrary-order accuracy can be achieved in meshless particle methods by combining Taylor-series expansion with least-squares techniques, this approach incurs high computational costs due to the inversion of high-order matrices. In this study, we develop a novel meshless method called least-square finite volume particle (LSFVP) method for solving PDEs efficiently. The particles are modeled as squares in two-dimensional space. The integral form of the PDEs is discretized for each finite volume particle using the LSFVP framework. The original second-order derivative is conceptually transformed into a first-order derivative. The least square method is employed to estimate the flux across particle surfaces, while Gauss integration ensures the overall second-order accuracy in evaluating surface flux integrals. Several numerical examples are presented to validate the proposed LSFVP method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"210 ","pages":"Pages 137-152"},"PeriodicalIF":2.5,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387827","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 : 2026-05-15Epub Date: 2026-03-03DOI: 10.1016/j.camwa.2026.02.016
Yuxiang Liang , Shun Zhang
A stationary Stokes problem with a piecewise constant viscosity coefficient with several subdomains is considered in the paper. For standard finite element pairs, a robust inf-sup condition is required to show the robustness of the discretization error with respect to the discontinuous viscosity, which has only been proven for the two-subdomain case in the paper [Numer. Math. (2006) 103: 129–149]. To avoid the robust inf-sup condition of a discrete finite element pair for multiple subdomains, we propose an ultra-weak augmented mixed finite element formulation. By adopting a Galerkin-least-squares method, the augmented mixed formulation can achieve stability without relying on the inf-sup condition in both continuous and discrete settings. The key step to have the robust a priori error estimate is that two norms, one energy norm and one full norm, are used in the robust continuity. The robust coercivity is proved for the energy norm. A robust a priori error estimate in the energy norm is then derived with the best approximation property in the full norm for the case of multiple subdomains. Additionally, the paper introduces a singular Kellogg-type example with exact solutions for the first time. Extensive numerical tests are conducted to validate the robust error estimate.
{"title":"Robust augmented mixed FEMs for stokes interface problems with discontinuous viscosity in multiple subdomains","authors":"Yuxiang Liang , Shun Zhang","doi":"10.1016/j.camwa.2026.02.016","DOIUrl":"10.1016/j.camwa.2026.02.016","url":null,"abstract":"<div><div>A stationary Stokes problem with a piecewise constant viscosity coefficient with several subdomains is considered in the paper. For standard finite element pairs, a robust inf-sup condition is required to show the robustness of the discretization error with respect to the discontinuous viscosity, which has only been proven for the two-subdomain case in the paper [Numer. Math. (2006) 103: 129–149]. To avoid the robust inf-sup condition of a discrete finite element pair for multiple subdomains, we propose an ultra-weak augmented mixed finite element formulation. By adopting a Galerkin-least-squares method, the augmented mixed formulation can achieve stability without relying on the inf-sup condition in both continuous and discrete settings. The key step to have the robust a priori error estimate is that two norms, one energy norm and one full norm, are used in the robust continuity. The robust coercivity is proved for the energy norm. A robust a priori error estimate in the energy norm is then derived with the best approximation property in the full norm for the case of multiple subdomains. Additionally, the paper introduces a singular Kellogg-type example with exact solutions for the first time. Extensive numerical tests are conducted to validate the robust error estimate.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"210 ","pages":"Pages 25-42"},"PeriodicalIF":2.5,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147359876","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 : 2026-05-15Epub Date: 2026-03-09DOI: 10.1016/j.camwa.2026.02.007
Yuwen Li, Yupeng Wang
In this article, we derive a novel convergence estimate for the weak POD-Greedy method with multiple POD modes and variable greedy thresholds in terms of the entropy numbers of the parametric solution manifold. Combining the POD with the Empirical Interpolation Method (EIM), we also propose an EIM-POD-Greedy method with entropy-based convergence analysis for simultaneously approximating parametrized target functions by separable approximants. Several numerical experiments are presented to demonstrate the effectiveness of the proposed algorithm compared to traditional methods.
{"title":"Some new convergence analysis and applications of POD-Greedy algorithms","authors":"Yuwen Li, Yupeng Wang","doi":"10.1016/j.camwa.2026.02.007","DOIUrl":"10.1016/j.camwa.2026.02.007","url":null,"abstract":"<div><div>In this article, we derive a novel convergence estimate for the weak POD-Greedy method with multiple POD modes and variable greedy thresholds in terms of the entropy numbers of the parametric solution manifold. Combining the POD with the Empirical Interpolation Method (EIM), we also propose an EIM-POD-Greedy method with entropy-based convergence analysis for simultaneously approximating parametrized target functions by separable approximants. Several numerical experiments are presented to demonstrate the effectiveness of the proposed algorithm compared to traditional methods.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"210 ","pages":"Pages 153-166"},"PeriodicalIF":2.5,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387828","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 : 2026-05-15Epub Date: 2026-03-04DOI: 10.1016/j.camwa.2026.02.017
Mario Kapl , Aljaž Kosmač , Vito Vitrih
We present a novel isogeometric collocation method for solving the Poisson’s and the biharmonic equation over planar bilinearly parameterized multi-patch geometries. The proposed approach relies on the use of a modified construction of the Cs-smooth mixed degree isogeometric spline space [1] for and in case of the Poisson’s and the biharmonic equation, respectively. The adapted spline space possesses the minimal possible degree everywhere on the multi-patch domain except in a small neighborhood of the inner edges and of the vertices of patch valency greater than one where a degree is required. This allows to solve the PDEs with a much lower number of degrees of freedom compared to employing the Cs-smooth spline space [2] with the same high degree everywhere. To perform isogeometric collocation with the smooth mixed degree spline functions, we introduce and study two different sets of collocation points, namely first a generalization of the standard Greville points to the set of mixed degree Greville points and second the so-called mixed degree superconvergent points. The collocation method is further extended to the class of bilinear-like Gs multi-patch parameterizations [3], which enables the modeling of multi-patch domains with curved boundaries, and is finally tested on the basis of several numerical examples.
{"title":"Isogeometric collocation with smooth mixed degree splines over planar multi-patch domains","authors":"Mario Kapl , Aljaž Kosmač , Vito Vitrih","doi":"10.1016/j.camwa.2026.02.017","DOIUrl":"10.1016/j.camwa.2026.02.017","url":null,"abstract":"<div><div>We present a novel isogeometric collocation method for solving the Poisson’s and the biharmonic equation over planar bilinearly parameterized multi-patch geometries. The proposed approach relies on the use of a modified construction of the <em>C<sup>s</sup></em>-smooth mixed degree isogeometric spline space [1] for <span><math><mrow><mi>s</mi><mo>=</mo><mn>2</mn></mrow></math></span> and <span><math><mrow><mi>s</mi><mo>=</mo><mn>4</mn></mrow></math></span> in case of the Poisson’s and the biharmonic equation, respectively. The adapted spline space possesses the minimal possible degree <span><math><mrow><mi>p</mi><mo>=</mo><mi>s</mi><mo>+</mo><mn>1</mn></mrow></math></span> everywhere on the multi-patch domain except in a small neighborhood of the inner edges and of the vertices of patch valency greater than one where a degree <span><math><mrow><mi>p</mi><mo>=</mo><mn>2</mn><mi>s</mi><mo>+</mo><mn>1</mn></mrow></math></span> is required. This allows to solve the PDEs with a much lower number of degrees of freedom compared to employing the <em>C<sup>s</sup></em>-smooth spline space [2] with the same high degree <span><math><mrow><mi>p</mi><mo>=</mo><mn>2</mn><mi>s</mi><mo>+</mo><mn>1</mn></mrow></math></span> everywhere. To perform isogeometric collocation with the smooth mixed degree spline functions, we introduce and study two different sets of collocation points, namely first a generalization of the standard Greville points to the set of mixed degree Greville points and second the so-called mixed degree superconvergent points. The collocation method is further extended to the class of bilinear-like <em>G<sup>s</sup></em> multi-patch parameterizations [3], which enables the modeling of multi-patch domains with curved boundaries, and is finally tested on the basis of several numerical examples.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"210 ","pages":"Pages 89-112"},"PeriodicalIF":2.5,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147359869","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 : 2026-05-15Epub Date: 2026-03-03DOI: 10.1016/j.camwa.2026.02.013
Haoyue Jiang , Hai-wei Sun , Yanbin Tang , Dan Zhao
This paper focuses on constructing and analyzing energy-stable schemes for the extended Fisher-Kolmogorov equation. The high-order difference methods are applied for the spatial discretization. And the exponential time difference (ETD) methods with a stabilized technique are used for the temporal discretization. Energy-stability of the fully-discrete scheme is proved. And the optimal L2 convergence results are obtained with help of the bounded numerical solutions and some inverse inequalities. Finally, several numerical experiments are presented to illustrate the theoretical results.
{"title":"Energy-stability and convergence of exponential difference schemes for extended Fisher-Kolmogorov equations","authors":"Haoyue Jiang , Hai-wei Sun , Yanbin Tang , Dan Zhao","doi":"10.1016/j.camwa.2026.02.013","DOIUrl":"10.1016/j.camwa.2026.02.013","url":null,"abstract":"<div><div>This paper focuses on constructing and analyzing energy-stable schemes for the extended Fisher-Kolmogorov equation. The high-order difference methods are applied for the spatial discretization. And the exponential time difference (ETD) methods with a stabilized technique are used for the temporal discretization. Energy-stability of the fully-discrete scheme is proved. And the optimal <em>L</em><sup>2</sup> convergence results are obtained with help of the bounded numerical solutions and some inverse inequalities. Finally, several numerical experiments are presented to illustrate the theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"210 ","pages":"Pages 60-75"},"PeriodicalIF":2.5,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147360835","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 : 2026-05-15Epub Date: 2026-03-03DOI: 10.1016/j.camwa.2026.01.039
Erli Wind-Andersen, Peter G. Petropoulos, Catalin Turc
We investigate high-order Convolution Quadratures methods for the solution of the wave equation in the exterior of two dimensional and axi-symmetric three dimensional scatterers that rely on Nyström discretizations for the Boundary Integral Equation formulations of the ensemble of associated Laplace domain modified Helmholtz problems. Both Dirichlet and Neumann boundary conditions, imposed on open-arc/open surfaces as well as Lipschitz closed scatterers, are considered. Two classes of CQ discretizations are employed, one based on linear multistep methods and the other based on Runge-Kutta methods, in conjunction with Nyström discretizations based on Alpert and QBX quadratures of Boundary Integral Equation (BIE) formulations of the Laplace domain Helmholtz problems with complex wavenumbers. A variety of accuracy tests are presented that showcase the high-order in time convergence (up to and including fifth order) that the Nyström CQ discretizations are capable of delivering and we compare to numerical results in the literature pertaining to time-domain multiple scattering problems solved with other methods.
{"title":"High-Order nyström/Convolution-Quadrature solution of time-Domain scattering from closed and open lipschitz boundaries with dirichlet and neumann boundary conditions","authors":"Erli Wind-Andersen, Peter G. Petropoulos, Catalin Turc","doi":"10.1016/j.camwa.2026.01.039","DOIUrl":"10.1016/j.camwa.2026.01.039","url":null,"abstract":"<div><div>We investigate high-order Convolution Quadratures methods for the solution of the wave equation in the exterior of two dimensional and axi-symmetric three dimensional scatterers that rely on Nyström discretizations for the Boundary Integral Equation formulations of the ensemble of associated Laplace domain modified Helmholtz problems. Both Dirichlet and Neumann boundary conditions, imposed on open-arc/open surfaces as well as Lipschitz closed scatterers, are considered. Two classes of CQ discretizations are employed, one based on linear multistep methods and the other based on Runge-Kutta methods, in conjunction with Nyström discretizations based on Alpert and QBX quadratures of Boundary Integral Equation (BIE) formulations of the Laplace domain Helmholtz problems with complex wavenumbers. A variety of accuracy tests are presented that showcase the high-order in time convergence (up to and including fifth order) that the Nyström CQ discretizations are capable of delivering and we compare to numerical results in the literature pertaining to time-domain multiple scattering problems solved with other methods.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"210 ","pages":"Pages 1-24"},"PeriodicalIF":2.5,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147359877","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 : 2026-05-15Epub Date: 2026-03-04DOI: 10.1016/j.camwa.2026.02.018
Raman Kumar , Gouranga Pradhan
This work presents a unified framework for generalized weak Galerkin (gWG) methods applied to two- and three-dimensional elliptic problems in the function spaces H(div), H(curl), and H(div, curl). The proposed methodology introduces generalized discrete differential operators, including weakly defined curl and divergence operators, within the weak Galerkin framework. A key feature of this approach is its flexibility in allowing arbitrary combinations of piecewise polynomial approximations in the interior and on the boundaries of each local polytopal element. Optimal order error estimates in energy norms are established for the resulting gWG method. Furthermore, numerical experiments are conducted to validate the theoretical findings and illustrate the accuracy and efficiency of the proposed method.
{"title":"Generalized weak Galerkin methods for H(div), H(curl), and H(div, curl)-elliptic problems","authors":"Raman Kumar , Gouranga Pradhan","doi":"10.1016/j.camwa.2026.02.018","DOIUrl":"10.1016/j.camwa.2026.02.018","url":null,"abstract":"<div><div>This work presents a unified framework for generalized weak Galerkin (gWG) methods applied to two- and three-dimensional elliptic problems in the function spaces <strong>H</strong>(div), <strong>H</strong>(curl), and <strong>H</strong>(div, curl). The proposed methodology introduces generalized discrete differential operators, including weakly defined curl and divergence operators, within the weak Galerkin framework. A key feature of this approach is its flexibility in allowing arbitrary combinations of piecewise polynomial approximations in the interior and on the boundaries of each local polytopal element. Optimal order error estimates in energy norms are established for the resulting gWG method. Furthermore, numerical experiments are conducted to validate the theoretical findings and illustrate the accuracy and efficiency of the proposed method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"210 ","pages":"Pages 76-88"},"PeriodicalIF":2.5,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147359871","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 : 2026-05-15Epub Date: 2026-03-05DOI: 10.1016/j.camwa.2026.02.014
M. Trezzi
We study a virtual element method for the Oseen problem. In the advection-dominated case, the method is stabilized with a three level jump of the convective term. To analyze the method, we prove specific estimates for the virtual space of potentials. Finally, we prove stability of the proposed method in the advection-dominated limit and derive h-version error estimates for the velocity and the pressure.
{"title":"A three-level CIP-VEM approach for the Oseen equation","authors":"M. Trezzi","doi":"10.1016/j.camwa.2026.02.014","DOIUrl":"10.1016/j.camwa.2026.02.014","url":null,"abstract":"<div><div>We study a virtual element method for the Oseen problem. In the advection-dominated case, the method is stabilized with a three level jump of the convective term. To analyze the method, we prove specific estimates for the virtual space of potentials. Finally, we prove stability of the proposed method in the advection-dominated limit and derive <em>h</em>-version error estimates for the velocity and the pressure.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"210 ","pages":"Pages 113-136"},"PeriodicalIF":2.5,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147360624","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 : 2026-05-01Epub Date: 2026-02-13DOI: 10.1016/j.camwa.2026.01.040
María González, Hiram Varela
We consider a primal-mixed finite element method proposed for the Darcy-Forchheimer model in [1]. We derive a new a posteriori error estimate and prove its reliability. We also provide some numerical experiments that show its performance in practice.
{"title":"Residual-type a posteriori error estimates for the Darcy-Forchheimer problem","authors":"María González, Hiram Varela","doi":"10.1016/j.camwa.2026.01.040","DOIUrl":"10.1016/j.camwa.2026.01.040","url":null,"abstract":"<div><div>We consider a primal-mixed finite element method proposed for the Darcy-Forchheimer model in [1]. We derive a new a posteriori error estimate and prove its reliability. We also provide some numerical experiments that show its performance in practice.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"209 ","pages":"Pages 28-43"},"PeriodicalIF":2.5,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146162098","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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