Domain decomposition type iterative techniques for parabolic problems on locally refined grids

Journal Article · Wed Dec 01 04:00:00 EST 1993 · SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics); (United States)

DOI:https://doi.org/10.1137/0730080· OSTI ID:5422830

Ewing, R E ^[1]; Lazarov, R D ^[2]; Pasciak, J E ^[3]; Vassilevski, P S ^[4]

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1. Texas A and M Univ., College Station, TX (United States). Inst. for Scientific Computation
2. Texas A and M Univ., College Station, TX (United States). Dept. of Mathematics
3. Brookhaven National Lab., Upton, NY (United States). Dept. of Applied Science
4. Univ. of California, Los Angeles, CA (United States). Dept. of Mathematics

Based on an extension of the discontinuous Galerkin finite element method, discretization scheme for solving parabolic problems on grids with local refinement, both in space and in time, are constructed. The stability of schemes constructed in this way is automatically ensured by the method. The construction of two-level preconditioners utilizing local time stepping and a global coarse-grid solver both on standard, rectangular, and uniform grids, is the main objective of the paper. The optimal convergence properties of such two-level preconditioners are studied. The theory is illustrated by a set of numerical examples.

• DOE Contract Number: AC02-76CH00016
• OSTI ID: 5422830
• Journal Information: SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics); (United States), Journal Name: SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics); (United States) Vol. 30:6; ISSN 0036-1429; ISSN SJNAAM
• Country of Publication: United States
• Language: English

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