A Posteriori Stopping Criteria for Optimized Schwarz Domain Decomposition Algorithms in Mixed Formulations

This paper develops a posteriori estimates for domain decomposition methods with optimized Robin transmission conditions on the interface between subdomains. We choose to demonstrate the methodology for mixed formulations, with a lowest-order Raviart–Thomas–Nédélec discretization, often used for het...

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Bibliographic Details
Published in:Journal of computational methods in applied mathematics Vol. 18; no. 3; pp. 495 - 519
Main Authors: Ali Hassan, Sarah, Japhet, Caroline, Kern, Michel, Vohralík, Martin
Format: Journal Article
Language:English
Published: Minsk De Gruyter 01.07.2018
Walter de Gruyter GmbH
Subjects:
65F10
65N15
65N22
65N55
76S05
A Posteriori Error Estimate
Adaptive algorithms
Decomposition
Discretization
Domain Decomposition Method, Optimized Schwarz Method
Domain decomposition methods
Heterogeneous Diffusion
Mixed Finite Element Method
Porous media
Robin Transmission Conditions
Stopping Criteria
ISSN:1609-4840, 1609-9389
Online Access:Get full text
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Summary:This paper develops a posteriori estimates for domain decomposition methods with optimized Robin transmission conditions on the interface between subdomains. We choose to demonstrate the methodology for mixed formulations, with a lowest-order Raviart–Thomas–Nédélec discretization, often used for heterogeneous and anisotropic porous media diffusion problems. Our estimators allow to distinguish the spatial discretization and the domain decomposition error components. We propose an adaptive domain decomposition algorithm wherein the iterations are stopped when the domain decomposition error does not affect significantly the overall error. Two main goals are thus achieved. First, a guaranteed bound on the overall error is obtained at each step of the domain decomposition algorithm. Second, important savings in terms of the number of domain decomposition iterations can be realized. Numerical experiments illustrate the efficiency of our estimates and the performance of the adaptive stopping criteria.
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ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2018-0010