Finite difference schemes on grids with local refinement in time and space for parabolic problems I. Derivation, stability, and error analysis

Computing ◽  
1990 ◽  
Vol 45 (3) ◽  
pp. 193-215 ◽  
Author(s):  
R. E. Ewing ◽  
R. D. Lazarov ◽  
P. S. Vassilevski
Keyword(s):  
Finite Difference ◽  
Error Analysis ◽  
Difference Schemes ◽  
Parabolic Problems ◽  
Finite Difference Schemes ◽  
Local Refinement ◽  
Time And Space ◽  
Stability And Error Analysis

PARALLEL DOMAIN DECOMPOSITION METHODS WITH THE OVERLAPPING OF SUBDOMAINS FOR PARABOLIC PROBLEMS

1996 ◽  
Vol 06 (08) ◽  
pp. 1169-1185 ◽  
Author(s):  
GRIGORII I. SHISHKIN ◽  
PETR N. VABISHCHEVICH
Keyword(s):  
Finite Difference ◽  
Domain Decomposition ◽  
Domain Decomposition Method ◽  
Approximate Solutions ◽  
Decomposition Methods ◽  
Difference Schemes ◽  
Parabolic Problems ◽  
Uniform Grid ◽  
Finite Difference Schemes ◽  
Dimensional Boundary

For a model of two-dimensional boundary value problem for a second-order parabolic equation, finite difference schemes on the base of a domain decomposition method, oriented on modern parallel computers, is constructed. In the used finite difference schemes iterations at time levels are not applied; some subdomains overlap. We study two classes of schemes characterized by synchronous and asynchronous implementations. It is shown that, under refining grids, the approximate solutions do converge to the exact one in the uniform grid norm.

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