ARBITRARY-ORDER NODAL MIMETIC DISCRETIZATIONS OF ELLIPTIC PROBLEMS ON POLYGONAL MESHES

被引：83

作者：

Da Veiga, L. Beirao ^{[1
]}

Lipnikov, K. ^{[2
]}

Manzini, G. ^{[3
]}

机构：

[1] Univ Milan, Dipartimento Matemat F Enriques, I-20133 Milan, Italy

[2] Los Alamos Natl Lab, Div Theoret, Los Alamos, NM 87545 USA

[3] CNR, Ist Matemat Applicata Tecnol Informat IMATI, I-27100 Pavia, Italy

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2011年 / 49卷 / 05期

关键词：

diffusion problem; Poisson equation; mimetic finite difference method; polygonal mesh; generalized mesh; high-order scheme; FINITE-DIFFERENCE METHOD; DIFFUSION-PROBLEMS; CONVERGENCE ANALYSIS; ELEMENT STRATEGY; ERROR ESTIMATOR; STOKES PROBLEM; APPROXIMATION;

D O I：

10.1137/100807764

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop and analyze a new family of mimetic methods on unstructured polygonal meshes for the diffusion problem in primal form. These methods are derived from the local consistency condition that is exact for polynomials of any degree m >= 1. The degrees of freedom are (a) solution values at the quadrature nodes of the Gauss-Lobatto formulas on each mesh edge, and (b) solution moments inside polygons. The convergence of the method is proven theoretically and an optimal error estimate is derived in a mesh-dependent norm that mimics the energy norm. Numerical experiments confirm the convergence rate that is expected from the theory.

引用

页码：1737 / 1760

页数：24

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