Abstract
In this paper, a posteriori error estimates for the generalized overlapping domain decomposition method with Dirichlet boundary conditions on the interfaces, for parabolic variational equation with second order boundary value problems, are derived using the semi-implicit-time scheme combined with a finite element spatial approximation. Furthermore a result of asymptotic behavior in uniform norm is given using Benssoussan-Lions’ algorithm.
Highlights
The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains
In [, ], an improved version of the Schwarz method for highly heterogeneous media has been presented. This method uses new optimized interface conditions specially designed to take into account the het
We develop an approach which combines a geometrical convergence result due to [, ] and a lemma which consists of estimating the error in the maximum norm between the continuous and discrete Schwarz iterates
Summary
The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. In [ ] the authors proved the error analysis in the maximum norm for a class of nonlinear elliptic problems in the context of overlapping nonmatching grids and they established the optimal L∞-error estimate between the discrete Schwarz sequence and the exact solution of the PDE, and in [ ] the authors derived a posteriori error estimates for the generalized overlapping domain decomposition method GODDM with Robin boundary conditions on the interfaces for second order boundary value problems; they have shown that the error estimate in the continuous case depends on the differences of the traces of the subdomain solutions on the interfaces after a discretization of the domain by finite elements method. In Section , an H ( )asymptotic behavior estimate for each subdomain is derived
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