Adjoint Based A Posteriori Analysis of Multiscale Mortar Discretizations with Multinumerics

Handle URI:
http://hdl.handle.net/10754/597464
Title:
Adjoint Based A Posteriori Analysis of Multiscale Mortar Discretizations with Multinumerics
Authors:
Tavener, Simon; Wildey, Tim
Abstract:
In this paper we derive a posteriori error estimates for linear functionals of the solution to an elliptic problem discretized using a multiscale nonoverlapping domain decomposition method. The error estimates are based on the solution of an appropriately defined adjoint problem. We present a general framework that allows us to consider both primal and mixed formulations of the forward and adjoint problems within each subdomain. The primal subdomains are discretized using either an interior penalty discontinuous Galerkin method or a continuous Galerkin method with weakly imposed Dirichlet conditions. The mixed subdomains are discretized using Raviart- Thomas mixed finite elements. The a posteriori error estimate also accounts for the errors due to adjoint-inconsistent subdomain discretizations. The coupling between the subdomain discretizations is achieved via a mortar space. We show that the numerical discretization error can be broken down into subdomain and mortar components which may be used to drive adaptive refinement.Copyright © by SIAM.
Citation:
Tavener S, Wildey T (2013) Adjoint Based A Posteriori Analysis of Multiscale Mortar Discretizations with Multinumerics. SIAM Journal on Scientific Computing 35: A2621–A2642. Available: http://dx.doi.org/10.1137/12089973X.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2013
DOI:
10.1137/12089973X
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This research was supported in part by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
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Full metadata record

DC FieldValue Language
dc.contributor.authorTavener, Simonen
dc.contributor.authorWildey, Timen
dc.date.accessioned2016-02-25T12:40:14Zen
dc.date.available2016-02-25T12:40:14Zen
dc.date.issued2013-01en
dc.identifier.citationTavener S, Wildey T (2013) Adjoint Based A Posteriori Analysis of Multiscale Mortar Discretizations with Multinumerics. SIAM Journal on Scientific Computing 35: A2621–A2642. Available: http://dx.doi.org/10.1137/12089973X.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/12089973Xen
dc.identifier.urihttp://hdl.handle.net/10754/597464en
dc.description.abstractIn this paper we derive a posteriori error estimates for linear functionals of the solution to an elliptic problem discretized using a multiscale nonoverlapping domain decomposition method. The error estimates are based on the solution of an appropriately defined adjoint problem. We present a general framework that allows us to consider both primal and mixed formulations of the forward and adjoint problems within each subdomain. The primal subdomains are discretized using either an interior penalty discontinuous Galerkin method or a continuous Galerkin method with weakly imposed Dirichlet conditions. The mixed subdomains are discretized using Raviart- Thomas mixed finite elements. The a posteriori error estimate also accounts for the errors due to adjoint-inconsistent subdomain discretizations. The coupling between the subdomain discretizations is achieved via a mortar space. We show that the numerical discretization error can be broken down into subdomain and mortar components which may be used to drive adaptive refinement.Copyright © by SIAM.en
dc.description.sponsorshipThis research was supported in part by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectAdjoint operatorsen
dc.subjectDiscontinuous Galerkin methodsen
dc.subjectError analysisen
dc.subjectMixed finite elementsen
dc.subjectMortar methodsen
dc.subjectMultinumericsen
dc.subjectMultiscaleen
dc.titleAdjoint Based A Posteriori Analysis of Multiscale Mortar Discretizations with Multinumericsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionColorado State University, Fort Collins, United Statesen
dc.contributor.institutionSandia National Laboratories, New Mexico, Albuquerque, United Statesen
kaust.grant.numberKUK-C1-013-04en
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