Uniformly Convergent Iterative Methods for Discontinuous Galerkin Discretizations

被引：34
|
作者：
Ayuso de Dios, Blanca [2 ]
Zikatanov, Ludmil [1 ]
机构：
[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA
[2] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2009年 / 40卷 / 1-3期
基金：
美国国家科学基金会;
关键词：
Discontinuous Galerkin finite element methods; Subspace correction methods; Interior Penalty methods; Iterative methods for non-symmetric problems; FINITE-ELEMENT METHODS; INTERIOR PENALTY; SCHWARZ PRECONDITIONERS; ELLIPTIC PROBLEMS; APPROXIMATIONS; DECOMPOSITION; ALGORITHMS;
D O I：
10.1007/s10915-009-9293-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present iterative and preconditioning techniques for the solution of the linear systems resulting from several discontinuous Galerkin (DG) Interior Penalty (IP) discretizations of elliptic problems. We analyze the convergence properties of these algorithms for both symmetric and non-symmetric IP schemes. The iterative methods are based on a "natural" decomposition of the first order DG finite element space as a direct sum of the Crouzeix-Raviart non-conforming finite element space and a subspace that contains functions discontinuous at interior faces. We also present numerical examples confirming the theoretical results.
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页码：4 / 36
页数：33
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