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Overlapping optimized Schwarz methods for parabolic equations in \(n\) dimensions. (English) Zbl 1263.35124

Summary: We introduce in this paper a new tool to prove the convergence of the overlapping optimized Schwarz methods with multisubdomains. The technique is based on some estimates of the errors on the boundaries of the overlapping strips. Our guiding example is an \(n\)-dimensional linear parabolic equation.

MSC:

35K10 Second-order parabolic equations
35A35 Theoretical approximation in context of PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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