CONVERGENCE ANALYSIS OF THE MIMETIC FINITE DIFFERENCE METHOD FOR ELLIPTIC PROBLEMS

被引：50

作者：

Cangiani, Andrea ^{[1
]}

Manzini, Gianmarco ^{[2
]}

Russo, Alessandro ^{[1
]}

机构：

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, I-20125 Milan, Italy

[2] CNR, IMATI, I-27100 Pavia, Italy

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2009年 / 47卷 / 04期

关键词：

mimetic finite difference method; boundary value problem; diffusion-convection-reaction equation; Raviart-Thomas finite element space; dual mixed formulation; polyhedral mesh; DIFFUSION DISCRETIZATION SCHEME; UNSTRUCTURED MESHES; VOLUME METHOD; OPERATORS; APPROXIMATION; EQUATION;

D O I：

10.1137/080717560

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a family of mimetic discretization schemes for elliptic problems including convection and reaction terms. Our approach is an extension of the mimetic methodology for purely diffusive problems on unstructured polygonal and polyhedral meshes. The a priori error analysis relies on the connection between the mimetic formulation and the lowest order Raviart-Thomas mixed finite element method. The theoretical results are confirmed by numerical experiments.

引用

页码：2612 / 2637

页数：26

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