Parallel Galerkin domain decomposition procedures for parabolic equation on general domain

• Published in: Numerical methods for partial differential equations Vol. 25; no. 5; pp. 1167 - 1194
• Main Authors: Ma, Keying, Sun, Tongjun, Yang, Danping
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01-09-2009
• Subjects: domain decomposition procedures; extrapolation method; Galerkin method; integral mean method; parabolic equation
• ISSN: 0749-159X; 1098-2426
• DOI: 10.1002/num.20394

Parallel Galerkin domain decomposition procedures for parabolic equation on general domain are given. These procedures use implicit Galerkin method in the subdomains and simple explicit flux calculation on the interdomain boundaries by integral mean method or extrapolation method to predict the inner‐boundary conditions. Thus, the parallelism can be achieved by these procedures. These procedures are conservative both in the subdomains and across interboundaries. The explicit nature of the flux prediction induces a time‐step limitation that is necessary to preserve stability, but this constraint is less severe than that for a fully explicit method. L2‐norm error estimates are derived for these procedures. Compared with the work of Dawson and Dupont [Math Comp 58 (1992), 21–35], these L2‐norm error estimates avoid the loss of H−1/2 factor. Experimental results are presented to confirm the theoretical results. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009