Explicit/implicit conservative Galerkin domain decomposition procedures for parabolic problems

Dawson, Clint N.; Dupont, Todd F.

doi:10.1090/S0025-5718-1992-1106964-9

Explicit/implicit conservative Galerkin domain decomposition procedures for parabolic problems

Authors: Clint N. Dawson and Todd F. Dupont
Journal: Math. Comp. 58 (1992), 21-34
MSC: Primary 65N55; Secondary 65N30
DOI: https://doi.org/10.1090/S0025-5718-1992-1106964-9
MathSciNet review: 1106964
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Several domain decomposition methods for approximating solutions of parabolic problems are given. These methods rely on implicit Galerkin procedures in the subdomains and explicit flux calculation on the inter-domain boundaries. The procedures are conservative both in the subdomains and across inter-domain boundaries. A priori error bounds and experimental results are presented.

[1] J. H. Bramble and A. H. Schatz, Higher order local accuracy by averaging in the finite element method, Math. Comp. 31 (1977), 94-111. MR 0431744 (55:4739)
[2] C. N. Dawson and Q. Du, A finite element domain decomposition method for parabolic equations, Rice Technical Report TR90-21, Dept. of Mathematical Sciences, Rice University, Houston, Texas.
[3] C. N. Dawson, Q. Du, and T. F. Dupont, A finite difference domain decomposition algorithm for numerical solution of the heat equation, Math. Comp. 57 (1991), 63-71. MR 1079011 (91m:65254)
[4] C. N. Dawson and T. F. Dupont, Explicit/implicit conservative domain decomposition procedures for parabolic problems in one space dimension (in preparation).
[5] T. F. Dupont and P. Keenan, An a priori estimate for variable-time-step second-order backward difference methods (in preparation).
[6] M. F. Wheeler, A priori ${L_2}$ error estimates for Galerkin approximations to parabolic partial differential equations, SIAM J. Numer. Anal. 10 (1973), 723-759. MR 0351124 (50:3613)