Pub Date : 2024-10-15DOI: 10.1016/j.camwa.2024.10.003
Jia Tan, Tian-jun Wang
The spectral collocation method coupled with domain decomposition is developed for solving the exterior problems of the Fisher's equation with polygon obstacles. Some results on the composite Laguerre-Legendre interpolation, which is a set of piecewise mixed interpolations coupled with domain decomposition, are introduced. As an important application, the composite spectral collocation scheme based on the Legendre-Gauss-Lobatto and the Laguerre-Gauss-Radau nodes is provided for the exterior problems of the Fisher's equation. The convergence of the proposed scheme is proved. Efficient algorithm is implemented. Numerical results demonstrate the high accuracy in space of the proposed method and confirm the theoretical analysis well. The approximation results and some techniques developed in this paper are also very useful for other exterior nonlinear problems with complex geometry.
{"title":"Spectral collocation method coupled with domain decomposition for exterior problems of the Fisher equation","authors":"Jia Tan, Tian-jun Wang","doi":"10.1016/j.camwa.2024.10.003","DOIUrl":"10.1016/j.camwa.2024.10.003","url":null,"abstract":"<div><div>The spectral collocation method coupled with domain decomposition is developed for solving the exterior problems of the Fisher's equation with polygon obstacles. Some results on the composite Laguerre-Legendre interpolation, which is a set of piecewise mixed interpolations coupled with domain decomposition, are introduced. As an important application, the composite spectral collocation scheme based on the Legendre-Gauss-Lobatto and the Laguerre-Gauss-Radau nodes is provided for the exterior problems of the Fisher's equation. The convergence of the proposed scheme is proved. Efficient algorithm is implemented. Numerical results demonstrate the high accuracy in space of the proposed method and confirm the theoretical analysis well. The approximation results and some techniques developed in this paper are also very useful for other exterior nonlinear problems with complex geometry.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142438438","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 : 2024-10-15DOI: 10.1016/j.camwa.2024.10.006
Lothar Nannen, Markus Wess
This paper introduces a method for computing eigenvalues and eigenvectors of a generalized Hermitian, matrix eigenvalue problem. The work is focused on large scale eigenvalue problems, where the application of a direct inverse is out of reach. Instead, an explicit time-domain integrator for the corresponding wave problem is combined with a proper filtering and a Krylov iteration in order to solve for eigenvalues within a given region of interest. We report results of small scale model problems to confirm the reliability of the method, as well as the computation of acoustic resonances in a three dimensional model of a hunting horn to demonstrate the efficiency.
{"title":"A Krylov eigenvalue solver based on filtered time domain solutions","authors":"Lothar Nannen, Markus Wess","doi":"10.1016/j.camwa.2024.10.006","DOIUrl":"10.1016/j.camwa.2024.10.006","url":null,"abstract":"<div><div>This paper introduces a method for computing eigenvalues and eigenvectors of a generalized Hermitian, matrix eigenvalue problem. The work is focused on large scale eigenvalue problems, where the application of a direct inverse is out of reach. Instead, an explicit time-domain integrator for the corresponding wave problem is combined with a proper filtering and a Krylov iteration in order to solve for eigenvalues within a given region of interest. We report results of small scale model problems to confirm the reliability of the method, as well as the computation of acoustic resonances in a three dimensional model of a hunting horn to demonstrate the efficiency.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-15DOI: 10.1016/j.camwa.2024.10.004
Tristan G. Vlogman, Kartik Jain
Many interesting particulate flow problems can only be studied using efficient numerical methods. We present a method based on a lattice Boltzmann fluid coupled to unresolved particles that interact with each other via the Discrete Element Method. Our method improves upon existing numerical schemes through the addition of a novel subcycling algorithm that guarantees momentum conservation during each DEM substep. The intended application is studying transport of solid particles in physiologic processes, although the method is generally applicable. We present in detail the development and (parallel) implementation of the model and show how intricacies of the coupling scheme must be considered to avoid unphysical behavior and instabilities. The scalability of the code is tested on two modern supercomputers. We demonstrate the method's applicability to biomedical applications by simulating the injection and distribution of particles in an idealized liver vasculature.
许多有趣的粒子流问题只能通过高效的数值方法进行研究。我们提出了一种基于晶格玻尔兹曼流体的方法，该流体与未解决的颗粒通过离散元素法相互作用。我们的方法改进了现有的数值方案，增加了新颖的子循环算法，保证了每个 DEM 子步骤中的动量守恒。该方法的预期应用是研究生理过程中固体颗粒的传输，尽管该方法普遍适用。我们详细介绍了该模型的开发和（并行）实施，并展示了必须如何考虑耦合方案的复杂性，以避免非物理行为和不稳定性。代码的可扩展性在两台现代超级计算机上进行了测试。我们通过模拟粒子在理想化肝脏血管中的注入和分布，展示了该方法在生物医学应用中的适用性。
{"title":"Efficient coupled lattice Boltzmann and Discrete Element Method simulations of small particles in complex geometries","authors":"Tristan G. Vlogman, Kartik Jain","doi":"10.1016/j.camwa.2024.10.004","DOIUrl":"10.1016/j.camwa.2024.10.004","url":null,"abstract":"<div><div>Many interesting particulate flow problems can only be studied using efficient numerical methods. We present a method based on a lattice Boltzmann fluid coupled to unresolved particles that interact with each other via the Discrete Element Method. Our method improves upon existing numerical schemes through the addition of a novel subcycling algorithm that guarantees momentum conservation during each DEM substep. The intended application is studying transport of solid particles in physiologic processes, although the method is generally applicable. We present in detail the development and (parallel) implementation of the model and show how intricacies of the coupling scheme must be considered to avoid unphysical behavior and instabilities. The scalability of the code is tested on two modern supercomputers. We demonstrate the method's applicability to biomedical applications by simulating the injection and distribution of particles in an idealized liver vasculature.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142438439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-15DOI: 10.1016/j.camwa.2024.10.002
Yanping Chen , Qiling Gu , Jian Huang
For the time fractional Allen-Cahn equation, integration of the exponential scalar auxiliary variable (ESAV) time discretization with the virtual element method (VEM) spatial discretization leads to ESAV-VEM schemes on polygonal meshes. The resulting ESAV-VEM algorithms are linear and effective for the completely decoupled computations of the phase variable u and the auxiliary variable r. Based on the positive definiteness of variable-step discrete convolution kernels relevant to L1 and L1-CN time discretizations, the corresponding unconditionally energy boundedness results are proven on arbitrary nonuniform time meshes. By means of the discrete gradient structure of the temporal discretization operator, the discrete energy dissipation laws are developed via a unified framework. Moreover, the discrete energy decay nature coincides with the classical analogies as the fractional order tends to one. Finally, a series of numerical experiments are presented to verify the accuracy and efficiency of the proposed method.
{"title":"Unconditionally energy stable ESAV-VEM schemes with variable time steps for the time fractional Allen-Cahn equation","authors":"Yanping Chen , Qiling Gu , Jian Huang","doi":"10.1016/j.camwa.2024.10.002","DOIUrl":"10.1016/j.camwa.2024.10.002","url":null,"abstract":"<div><div>For the time fractional Allen-Cahn equation, integration of the exponential scalar auxiliary variable (ESAV) time discretization with the virtual element method (VEM) spatial discretization leads to ESAV-VEM schemes on polygonal meshes. The resulting ESAV-VEM algorithms are linear and effective for the completely decoupled computations of the phase variable <em>u</em> and the auxiliary variable <em>r</em>. Based on the positive definiteness of variable-step discrete convolution kernels relevant to L1 and L1-CN time discretizations, the corresponding unconditionally energy boundedness results are proven on arbitrary nonuniform time meshes. By means of the discrete gradient structure of the temporal discretization operator, the discrete energy dissipation laws are developed via a unified framework. Moreover, the discrete energy decay nature coincides with the classical analogies as the fractional order tends to one. Finally, a series of numerical experiments are presented to verify the accuracy and efficiency of the proposed method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142438437","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 : 2024-10-14DOI: 10.1016/j.camwa.2024.10.008
Yongseok Jang, Emeric Martin, Jean-Baptiste Chapelier, Vincent Couaillier
We present a novel approach utilizing two-level dynamic load balancing for p-adaptive discontinuous Galerkin (DG) methods in compressible Computational Fluid Dynamics (CFD) simulations. The high-order explicit first stage, specifically the singly diagonal implicit Runge–Kutta (ESDIRK) method, is employed for time integration, where the pseudo-transient continuation is integrated with the restarted generalized minimal residual (GMRES) method to handle the solution of nonlinear equations at each stage of ESDIRK, excluding the initial stage. Relying on smoothness indicators, we carry out the refinement/coarsening process for p-adaptation with dynamic load balancing. This approach involves a coarse level (distributed memory) decomposition based on MPI paradigm and a fine level (shared memory) decomposition based on OpenMP paradigm, enhancing parallel efficiency. Dynamic load balancing is achieved by computing weights based on degrees of freedom, ensuring balanced computational loads across processors. The parallel computing framework adopts either a graph-based type (ParMETIS and Zoltan) or space-filling curves type (GeMPa) for coarse level partitioning, and a graph-based type (METIS and Zoltan) for fine level partitioning. The effectiveness of the method is demonstrated through numerical examples, highlighting its potential to significantly improve the scalability and efficiency of compressible flow simulations. The numerical simulations were conducted using the CODA flow solver, a state-of-the-art tool developed collaboratively by the French National Aerospace Center (ONERA), the German Aerospace Center (DLR), and Airbus.
{"title":"Two-level dynamic load-balanced p-adaptive discontinuous Galerkin methods for compressible CFD simulations","authors":"Yongseok Jang, Emeric Martin, Jean-Baptiste Chapelier, Vincent Couaillier","doi":"10.1016/j.camwa.2024.10.008","DOIUrl":"10.1016/j.camwa.2024.10.008","url":null,"abstract":"<div><div>We present a novel approach utilizing two-level dynamic load balancing for <em>p</em>-adaptive discontinuous Galerkin (DG) methods in compressible Computational Fluid Dynamics (CFD) simulations. The high-order explicit first stage, specifically the singly diagonal implicit Runge–Kutta (ESDIRK) method, is employed for time integration, where the pseudo-transient continuation is integrated with the restarted generalized minimal residual (GMRES) method to handle the solution of nonlinear equations at each stage of ESDIRK, excluding the initial stage. Relying on smoothness indicators, we carry out the refinement/coarsening process for <em>p</em>-adaptation with dynamic load balancing. This approach involves a coarse level (distributed memory) decomposition based on MPI paradigm and a fine level (shared memory) decomposition based on OpenMP paradigm, enhancing parallel efficiency. Dynamic load balancing is achieved by computing weights based on degrees of freedom, ensuring balanced computational loads across processors. The parallel computing framework adopts either a graph-based type (ParMETIS and Zoltan) or space-filling curves type (GeMPa) for coarse level partitioning, and a graph-based type (METIS and Zoltan) for fine level partitioning. The effectiveness of the method is demonstrated through numerical examples, highlighting its potential to significantly improve the scalability and efficiency of compressible flow simulations. The numerical simulations were conducted using the CODA flow solver, a state-of-the-art tool developed collaboratively by the French National Aerospace Center (ONERA), the German Aerospace Center (DLR), and Airbus.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-10DOI: 10.1016/j.camwa.2024.10.001
Lucas Silveira Campos, Carlos Friedrich Loeffler
This study introduces a new modelling approach that leads to a more efficient process for constructing the matrix system arising from the discretization of integral equations by the boundary element method. This method uses the matrix structure employed in the direct interpolation technique, yielding computational efficiency while maintaining precise outcomes and ensuring convergence as the mesh is refined. To demonstrate the effectiveness of this novel numerical technique, it is applied to solve two-dimensional problems governed by the Laplace equation.
{"title":"A new strategy for a faster matrix assembly in the boundary element method","authors":"Lucas Silveira Campos, Carlos Friedrich Loeffler","doi":"10.1016/j.camwa.2024.10.001","DOIUrl":"10.1016/j.camwa.2024.10.001","url":null,"abstract":"<div><div>This study introduces a new modelling approach that leads to a more efficient process for constructing the matrix system arising from the discretization of integral equations by the boundary element method. This method uses the matrix structure employed in the direct interpolation technique, yielding computational efficiency while maintaining precise outcomes and ensuring convergence as the mesh is refined. To demonstrate the effectiveness of this novel numerical technique, it is applied to solve two-dimensional problems governed by the Laplace equation.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421916","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 : 2024-10-08DOI: 10.1016/j.camwa.2024.09.025
Yanli Chen , Xin Liu , Wenhui Zhang , Yufeng Nie
This work introduces and analyzes the mixed virtual element method on polygonal meshes for the numerical discretization of poro-elastodynamics models. For spatial discretization, we employ the mixed virtual element method on polygonal meshes, coupled with Newmark-β integration schemes for time discretization. We present a stability analysis for both the continuous and semi-discrete problems and derive error estimates for the energy norm in the semi-discrete case. Numerical experiments are conducted to verify the theoretical analysis, and the results on Voronoi meshes demonstrate that the algorithm effectively handles various dynamic viscosities.
{"title":"Mixed virtual element methods for the poro-elastodynamics model on polygonal grids","authors":"Yanli Chen , Xin Liu , Wenhui Zhang , Yufeng Nie","doi":"10.1016/j.camwa.2024.09.025","DOIUrl":"10.1016/j.camwa.2024.09.025","url":null,"abstract":"<div><div>This work introduces and analyzes the mixed virtual element method on polygonal meshes for the numerical discretization of poro-elastodynamics models. For spatial discretization, we employ the mixed virtual element method on polygonal meshes, coupled with Newmark-<em>β</em> integration schemes for time discretization. We present a stability analysis for both the continuous and semi-discrete problems and derive error estimates for the energy norm in the semi-discrete case. Numerical experiments are conducted to verify the theoretical analysis, and the results on Voronoi meshes demonstrate that the algorithm effectively handles various dynamic viscosities.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421915","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 : 2024-10-08DOI: 10.1016/j.camwa.2024.09.023
Caixia Nan , Qian Zhang
The elastic bending energy model is commonly used to describe the shape transformation of biological lipid vesicles, making it a classical phase field model. In this paper, by coupling the elastic bending energy with the total variation (TV) regularization, we develop an elastic bending-TV model for image inpainting. By solving the energy minimization problem of this model, we obtain the results for image processing. We adopt an operator splitting method for the model and the numerical scheme involves the introduction of two vector- and scalar-valued functions to reconstruct this functional. The energy minimization problem is transformed into finding the steady state solution of artificial time-dependent PDE systems. At each fractional step, we can find either a closed-form solution or being solved by an efficient algorithm, which is a very robust and stable algorithm. Experimental results validate the superiority of our model and the effectiveness of the scheme for image inpainting.
{"title":"Elastic bending total variation model for image inpainting with operator splitting method","authors":"Caixia Nan , Qian Zhang","doi":"10.1016/j.camwa.2024.09.023","DOIUrl":"10.1016/j.camwa.2024.09.023","url":null,"abstract":"<div><div>The elastic bending energy model is commonly used to describe the shape transformation of biological lipid vesicles, making it a classical phase field model. In this paper, by coupling the elastic bending energy with the total variation (TV) regularization, we develop an elastic bending-TV model for image inpainting. By solving the energy minimization problem of this model, we obtain the results for image processing. We adopt an operator splitting method for the model and the numerical scheme involves the introduction of two vector- and scalar-valued functions to reconstruct this functional. The energy minimization problem is transformed into finding the steady state solution of artificial time-dependent PDE systems. At each fractional step, we can find either a closed-form solution or being solved by an efficient algorithm, which is a very robust and stable algorithm. Experimental results validate the superiority of our model and the effectiveness of the scheme for image inpainting.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421297","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 : 2024-10-08DOI: 10.1016/j.camwa.2024.09.032
Yiyang Wang, Zhongguo Zhou
In this paper, the mass conservative characteristic finite difference scheme for 2-d advection diffusion equations is analyzed. Firstly, along x-direction, we obtain the solutions by applying the piecewise parabolic method (PPM) on the Lagrangian grid where is solved using the first-order Runge Kutta scheme. Secondly, the mass over are solved by the PPM scheme along y-direction. Finally, the local conservative characteristic finite difference scheme is constructed. By some auxiliary lemmas, we prove our scheme is stable and obtain the optimal error estimate. Our scheme is proved to be of second order convergence in space and of first order in time. Numerical experiments are used to verify the theoretical analysis.
本文分析了二维平流扩散方程的质量守恒特征有限差分方案。首先，沿 x 方向，在拉格朗日网格上应用片断抛物线法（PPM）得到解 {U˜i,jn}，其中 x¯ 采用一阶 Runge Kutta 方案求解。其次，采用 PPM 方案沿 y 方向求解 Ω¯i,j(tn)上的质量 M¯i,jn。最后，构建局部保守特征有限差分方案。通过一些辅助定理，我们证明了我们的方案是稳定的，并得到了最优误差估计。我们的方案在空间上具有二阶收敛性，在时间上具有一阶收敛性。数值实验用于验证理论分析。
{"title":"Theoretical analysis and numerical scheme of local conservative characteristic finite difference for 2-d advection diffusion equations","authors":"Yiyang Wang, Zhongguo Zhou","doi":"10.1016/j.camwa.2024.09.032","DOIUrl":"10.1016/j.camwa.2024.09.032","url":null,"abstract":"<div><div>In this paper, the mass conservative characteristic finite difference scheme for 2-d advection diffusion equations is analyzed. Firstly, along <em>x</em>-direction, we obtain the solutions <span><math><mo>{</mo><msubsup><mrow><mover><mrow><mi>U</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow><mrow><mi>n</mi></mrow></msubsup><mo>}</mo></math></span> by applying the piecewise parabolic method (PPM) on the Lagrangian grid where <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span> is solved using the first-order Runge Kutta scheme. Secondly, the mass <span><math><msubsup><mrow><mover><mrow><mi>M</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> over <span><math><msub><mrow><mover><mrow><mi>Ω</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>(</mo><msup><mrow><mi>t</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> are solved by the PPM scheme along <em>y</em>-direction. Finally, the local conservative characteristic finite difference scheme is constructed. By some auxiliary lemmas, we prove our scheme is stable and obtain the optimal error estimate. Our scheme is proved to be of second order convergence in space and of first order in time. Numerical experiments are used to verify the theoretical analysis.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419165","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 : 2024-10-08DOI: 10.1016/j.camwa.2024.09.031
Jeonghun J. Lee
In this work we develop an a posteriori error estimator for mixed finite element methods of Darcy flow problems with Robin-type jump interface conditions. We construct an energy-norm type a posteriori error estimator using the Stenberg post-processing. The reliability of the estimator is proved using an interface-adapted Helmholtz-type decomposition and an interface-adapted Scott–Zhang type interpolation operator. A local efficiency and the reliability of post-processed pressure are also proved. Numerical results illustrating adaptivity algorithms using our estimator are included.
{"title":"A posteriori error estimates of Darcy flows with Robin-type jump interface conditions","authors":"Jeonghun J. Lee","doi":"10.1016/j.camwa.2024.09.031","DOIUrl":"10.1016/j.camwa.2024.09.031","url":null,"abstract":"<div><div>In this work we develop an a posteriori error estimator for mixed finite element methods of Darcy flow problems with Robin-type jump interface conditions. We construct an energy-norm type a posteriori error estimator using the Stenberg post-processing. The reliability of the estimator is proved using an interface-adapted Helmholtz-type decomposition and an interface-adapted Scott–Zhang type interpolation operator. A local efficiency and the reliability of post-processed pressure are also proved. Numerical results illustrating adaptivity algorithms using our estimator are included.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421914","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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