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A second-order overlapping Schwarz method for a 2d singularly perturbed semilinear reaction-diffusion problem

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Show simple item record Kopteva, Natalia Pickett, Maria 2017-05-04T12:02:26Z 2017-05-04T12:02:26Z 2012
dc.description peer-reviewed en_US
dc.description.abstract An overlapping Schwarz domain decomposition is applied to a semilinear reaction-diffusion equation posed in a smooth two-dimensional domain. The problem may exhibit multiple solutions; its diffusion parameter epsilon(2) is arbitrarily small, which induces boundary layers. The Schwarz method invokes a boundary-layer subdomain and an interior subdomain, the narrow subdomain overlap being of width O(epsilon vertical bar ln h vertical bar), where h is the maximum side length of mesh elements, and the global number of mesh nodes does not exceed O(h(-2)). We employ finite differences on layer-adapted meshes of Bakhvalov and Shishkin types in the boundary-layer subdomain, and lumped-mass linear finite elements on a quasiuniform Delaunay triangulation in the interior subdomain. For this iterative method, we present maximum norm error estimates for epsilon is an element of (0, 1]. It is shown, in particular, that when epsilon <= C vertical bar ln h vertical bar(-1), one iteration is sufficient to get second-order convergence (with, in the case of the Shishkin mesh, a logarithmic factor) in the maximum norm uniformly in E. Numerical results are presented to support our theoretical conclusions. en_US
dc.language.iso eng en_US
dc.publisher American Mathematical Society en_US
dc.relation.ispartofseries Mathematics of Computation;81, pp. 81-105
dc.rights First published in Mathematics of Computation, 81, pp. 81-105, 2012, published by the American Mathematical Society en_US
dc.subject singular perturbation en_US
dc.subject domain decomposition en_US
dc.subject overlapping Schwarz en_US
dc.subject Bakhvalov mesh en_US
dc.subject Shishkin mesh en_US
dc.subject supra-convergence en_US
dc.title A second-order overlapping Schwarz method for a 2d singularly perturbed semilinear reaction-diffusion problem en_US
dc.type info:eu-repo/semantics/article en_US
dc.type.supercollection all_ul_research en_US
dc.type.supercollection ul_published_reviewed en_US 2017-04-28T13:57:14Z
dc.description.version ACCEPTED
dc.identifier.doi 10.1090/S0025-5718-2011-02521-4
dc.contributor.sponsor IRC en_US
dc.contributor.sponsor SFI en_US
dc.rights.accessrights info:eu-repo/semantics/openAccess en_US
dc.internal.rssid 1387505
dc.internal.copyrightchecked Yes
dc.identifier.journaltitle Mathematics Of Computation
dc.description.status peer-reviewed

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