A new discretization methodology for diffusion problems on generalized polyhedral meshes

被引：113
|
作者：
Brezzi, Franco
Lipnikov, Konstantin
Shashkov, Mikhail
Simoncini, Valeria
机构：
[1] Los Alamos Natl Lab, Div Theoret, Los Alamos, NM 87545 USA
[2] Ist Univ Super, CeSNA, Pavia, Italy
[3] Univ Bologna, Dipartmento Matemat, CIRSA, Ravenna, Italy
[4] IMATI CNR, Pavia, Italy
来源：
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2007年 / 196卷 / 37-40期
关键词：
finite difference; compatible discretizations; polyhedral meshes;
D O I：
10.1016/j.cma.2006.10.028
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
We develop a family of inexpensive discretization schemes for diffusion problems on generalized polyhedral meshes with elements having non-planar faces. The material properties are described by a full tensor. We also prove superconvergence for the scalar (pressure) variable under very general assumptions. The theoretical results are confirmed with numerical experiments. In the practically important case of logically cubic meshes with randomly perturbed nodes, the mixed finite element with the lowest order Raviart-Thomas elements does not converge while the proposed mimetic method has the optimal convergence rate. (c) 2007 Elsevier B.V. All rights reserved.
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页码：3682 / 3692
页数：11
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