A VIRTUAL VOLUME METHOD FOR HETEROGENEOUS AND ANISOTROPIC DIFFUSION-REACTION PROBLEMS ON GENERAL MESHES

Coatleven Julien

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A VIRTUAL VOLUME METHOD FOR HETEROGENEOUS AND ANISOTROPIC DIFFUSION-REACTION PROBLEMS ON GENERAL MESHES

机译：一种虚拟体积法，用于一般网格的异质和各向异性扩散 - 反应问题

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Starting from the recently introduced virtual element method, we construct new diffusion fluxes in two and three dimensions that give birth to symmetric, unconditionally coercive finite volume like schemes for the discretization of heterogeneous and anisotropic diffusion-reaction problems on general, possibly nonconforming meshes. Convergence of the approximate solutions is proved for general tensors and meshes. Error estimates are derived under classical regularity assumptions. Numerical results illustrate the performance of the scheme. The link with the original vertex approximate gradient scheme is emphasized.

机译：从最近引入的虚拟元素方法开始，我们构建了两个和三个维度的新扩散通量，该尺寸为一般，可能是不合格网格的离散化的关于异质和各向异性扩散反应问题的方案。对一般张量和网格证明了近似解的融合。错误估计在古典规则假设下派生。数值结果说明了该方案的性能。强调了具有原始顶点近似梯度方案的链接。

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来源
《ESAIM. Mathematical modelling and numerical analysis》 |2017年第3期|共28页
作者
Coatleven Julien;
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作者单位

IFP Energies Nouvelles 1 &

4 Ave Bois Preau F-92852 Rueil Malmaison France;

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原文格式 PDF
正文语种 eng
中图分类模型理论;数值分析;
关键词
Heterogeneous diffusion-reaction problems; finite volumes; general meshes; virtual element method;

机译：异质扩散反应问题;有限卷;一般网格;虚拟元素方法;

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1. A VIRTUAL VOLUME METHOD FOR HETEROGENEOUS AND ANISOTROPIC DIFFUSION-REACTION PROBLEMS ON GENERAL MESHES [J] . Coatleven Julien ESAIM. Mathematical modelling and numerical analysis . 2017,第3期

机译：一种虚拟体积法，用于一般网格的异质和各向异性扩散 - 反应问题
2. Convergence of nonlinear finite volume schemes for heterogeneous anisotropic diffusion on general meshes [J] . Martin Schneider, Léo Agélas, Guillaume Enchéry, Journal of Computational Physics . 2017,第期

机译：一般网眼非均相各向异性扩散的非线性有限体积方案的收敛性
3. Convergence of the finite volume MPFA O scheme for heterogeneous anisotropic diffusion problems on general meshes [J] . Agelas L, Masson R Comptes rendus. Mathematique . 2008,第17a18期

机译：一般网格上非均质各向异性扩散问题的有限体积MPFA O格式的收敛性
4. Heterogeneous CPU-GPU computing for the finite volume method on 3D unstructured meshes [C] . Langguth Johannes, Xing Cai IEEE International Conference on Parallel and Distributed Systems . 2014

机译：3D非结构化网格上有限体积方法的异构CPU-GPU计算
5. A coupled local mode approach to laterally heterogeneous anisotropic media, volume scattering, and T-wave excitation. [D] . Soukup, Darin J. 2004

机译：一种耦合的局部模式方法，用于横向非均质各向异性介质，体积散射和T波激发。
6. Database Methods and Delivery. Integrating Heterogeneous Resources: The Integrated Academic Information Management Systems (IAIMS): BioSYNTHESIS: Integrating Multiple Databases into a Virtual Database [O] . Naomi C. Broering, Helen Bagdoyan, Jeffrey Hylton, 1989

机译：数据库方法和交付。集成异构资源：集成学术信息管理系统（IAIMS）：BioSYNTHESIS：将多个数据库集成到虚拟数据库中
7. Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes [O] . Di Pietro Daniele Antonio, Ern Alexandre 2017

机译：一般网格上非均质各向异性扩散的任意阶混合方法
8. Finite Volume Methods, Unstructured Meshes and Strict Stability. [R] . Adamsson, C., Forsberg, K., Nordstroem, J. 2001

机译：有限体积法，非结构网格和严格稳定性。

A VIRTUAL VOLUME METHOD FOR HETEROGENEOUS AND ANISOTROPIC DIFFUSION-REACTION PROBLEMS ON GENERAL MESHES

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