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

MathSciNet review:
1106964

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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), no. 137, 94–111. MR**0431744**, 10.1090/S0025-5718-1977-0431744-9**[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]**Clint N. Dawson, Qiang Du, and Todd F. Dupont,*A finite difference domain decomposition algorithm for numerical solution of the heat equation*, Math. Comp.**57**(1991), no. 195, 63–71. MR**1079011**, 10.1090/S0025-5718-1991-1079011-4**[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]**Mary Fanett Wheeler,*A priori 𝐿₂ error estimates for Galerkin approximations to parabolic partial differential equations*, SIAM J. Numer. Anal.**10**(1973), 723–759. MR**0351124**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1992-1106964-9

Keywords:
Domain decomposition,
parabolic equations,
finite elements,
parallel computing

Article copyright:
© Copyright 1992
American Mathematical Society