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Open Access Research

A BDDC algorithm for the mortar-type rotated Q1 FEM for elliptic problems with discontinuous coefficients

Yaqin Jiang1 and Jinru Chen2

Author Affiliations

1 School of Sciences, Nanjing University of Posts and Telecommunications, Nanjing, 210046, P.R. China

2 Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210046, P.R. China

Boundary Value Problems 2014, 2014:79  doi:10.1186/1687-2770-2014-79

Published: 3 April 2014

Abstract

In this paper, we propose a BDDC preconditioner for the mortar-type rotated <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/79/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/79/mathml/M1">View MathML</a> finite element method for second order elliptic partial differential equations with piecewise but discontinuous coefficients. We construct an auxiliary discrete space and build our algorithm on an equivalent auxiliary problem, and we present the BDDC preconditioner based on this constructed discrete space. Meanwhile, in the framework of the standard additive Schwarz methods, we describe this method by a complete variational form. We show that our method has a quasi-optimal convergence behavior, i.e., the condition number of the preconditioned problem is independent of the jumps of the coefficients, and depends only logarithmically on the ratio between the subdomain size and the mesh size. Numerical experiments are presented to confirm our theoretical analysis.

MSC: 65N55, 65N30.

Keywords:
domain decomposition; BDDC algorithm; mortar; rotated <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/79/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/79/mathml/M1">View MathML</a> element; preconditioner