Domain decomposition methods for the diffusion equation with low-regularity solution

被引:20
作者
Ciarlet, P., Jr. [1 ]
Jamelot, E. [2 ]
Kpadonou, F. D. [3 ]
机构
[1] Univ Paris Saclay, CNRS, POEMS, ENSTA ParisTech,INRIA, 828 Bd Marechaux, F-91762 Palaiseau, France
[2] CEA Saclay, Commissariat Energie Atom & Energie Alternat, F-91191 Gif Sur Yvette, France
[3] UVSQ, Lab Math Versailles, 45 Av Etats Unis, F-78035 Versailles, France
关键词
Diffusion equation; Low-regularity solution; Mixed formulation; Domain decomposition methods; FINITE-ELEMENT METHODS; APPROXIMATION; BOUNDARY; MEDIA;
D O I
10.1016/j.camwa.2017.07.017
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We analyze matching and non-matching domain decomposition methods for the numerical approximation of the mixed diffusion equations. Special attention is paid to the case where the solution is of low regularity. Such a situation commonly arises in the presence of three or more intersecting material components with different characteristics. The domain decomposition method can be non-matching in the sense that the traces of the finite element spaces may not fit at the interface between subdomains. We prove well-posedness of the discrete problem, that is solvability of the corresponding linear system, provided two algebraic conditions are fulfilled. If moreover the conditions hold independently of the discretization, convergence is ensured. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码:2369 / 2384
页数:16
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