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A finite difference non-overlapping non-matching domain decomposition algorithm for heat equation. (English) Zbl 1176.65091
Summary: In this paper, we provide a maximum norm analysis of a finite difference scheme defined on non-overlapping non-matching grid for the heat equation. We consider a domain decomposition which each subdomain has its own independently generated grid. The grid points on the subdomain boundaries need not match the grid points from adjacent subdomain. In this procedure, interface values between subdomain are found by an explicit finite difference formula. Once these values are calculated, interior values are determined by backward differencing in time. Maximum norm error estimates for these procedures are derived.
MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer
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