A two-level method for mimetic finite difference discretizations of elliptic problems

被引：4

作者：

Antonietti, Paola F. ^{[1
]}

Verani, Marco ^{[1
]}

Zikatanov, Ludmil ^{[2
,3
]}

机构：

[1] Politecn Milan, Dipartimento Matemat, MOX, I-20133 Milan, Italy

[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[3] Bulgarian Acad Sci, Inst Math & Informat, BU-1113 Sofia, Bulgaria

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2015年 / 70卷 / 11期

基金：

美国国家科学基金会;

关键词：

Mimetic finite differences; Two-level preconditioners; DIFFUSION-PROBLEMS; STOKES PROBLEM; CONVERGENCE; APPROXIMATION; ELEMENTS; SPACES;

D O I：

10.1016/j.camwa.2015.06.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose and analyze a two-level method for mimetic finite difference approximations of second order elliptic boundary value problems. We prove that the two-level algorithm is uniformly convergent, i.e., the number of iterations needed to achieve convergence is uniformly bounded independently of the characteristic size of the underlying partition. We also show that the resulting scheme provides a uniform preconditioner with respect to the number of degrees of freedom. Numerical results that validate the theory are also presented. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：2674 / 2687

页数：14

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