Adjoint-Based a Posteriori Error Estimation for Coupled Time-Dependent Systems

Handle URI:
http://hdl.handle.net/10754/597466
Title:
Adjoint-Based a Posteriori Error Estimation for Coupled Time-Dependent Systems
Authors:
Asner, Liya; Tavener, Simon; Kay, David
Abstract:
We consider time-dependent parabolic problem s coupled across a common interface which we formulate using a Lagrange multiplier construction and solve by applying a monolithic solution technique. We derive an adjoint-based a posteriori error representation for a quantity of interest given by a linear functional of the solution. We establish the accuracy of our error representation formula through numerical experimentation and investigate the effect of error in the adjoint solution. Crucially, the error representation affords a distinction between temporal and spatial errors and can be used as a basis for a blockwise time-space refinement strategy. Numerical tests illustrate the efficacy of the refinement strategy by capturing the distinctive behavior of a localized traveling wave solution. The saddle point systems considered here are equivalent to those arising in the mortar finite element technique for parabolic problems. © 2012 Society for Industrial and Applied Mathematics.
Citation:
Asner L, Tavener S, Kay D (2012) Adjoint-Based a Posteriori Error Estimation for Coupled Time-Dependent Systems. SIAM Journal on Scientific Computing 34: A2394–A2419. Available: http://dx.doi.org/10.1137/110858458.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2012
DOI:
10.1137/110858458
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This work was supported in part by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).The first author's work is supported by the Clarendon Fund, University of Oxford, and by the Scatcherd European Scholarship.
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorAsner, Liyaen
dc.contributor.authorTavener, Simonen
dc.contributor.authorKay, Daviden
dc.date.accessioned2016-02-25T12:40:17Zen
dc.date.available2016-02-25T12:40:17Zen
dc.date.issued2012-01en
dc.identifier.citationAsner L, Tavener S, Kay D (2012) Adjoint-Based a Posteriori Error Estimation for Coupled Time-Dependent Systems. SIAM Journal on Scientific Computing 34: A2394–A2419. Available: http://dx.doi.org/10.1137/110858458.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/110858458en
dc.identifier.urihttp://hdl.handle.net/10754/597466en
dc.description.abstractWe consider time-dependent parabolic problem s coupled across a common interface which we formulate using a Lagrange multiplier construction and solve by applying a monolithic solution technique. We derive an adjoint-based a posteriori error representation for a quantity of interest given by a linear functional of the solution. We establish the accuracy of our error representation formula through numerical experimentation and investigate the effect of error in the adjoint solution. Crucially, the error representation affords a distinction between temporal and spatial errors and can be used as a basis for a blockwise time-space refinement strategy. Numerical tests illustrate the efficacy of the refinement strategy by capturing the distinctive behavior of a localized traveling wave solution. The saddle point systems considered here are equivalent to those arising in the mortar finite element technique for parabolic problems. © 2012 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis work was supported in part by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).The first author's work is supported by the Clarendon Fund, University of Oxford, and by the Scatcherd European Scholarship.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectA posteriori error analysisen
dc.subjectAdjoint problemen
dc.subjectCoupled problemen
dc.subjectMesh refinementen
dc.subjectMortar finite elementsen
dc.titleAdjoint-Based a Posteriori Error Estimation for Coupled Time-Dependent Systemsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionColorado State University, Fort Collins, United Statesen
kaust.grant.numberKUK-C1-013-04en
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