A class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity

Handle URI:
http://hdl.handle.net/10754/597230
Title:
A class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity
Authors:
Demkowicz, Leszek; Gopalakrishnan, Jay; Niemi, Antti H.
Abstract:
We continue our theoretical and numerical study on the Discontinuous Petrov-Galerkin method with optimal test functions in context of 1D and 2D convection-dominated diffusion problems and hp-adaptivity. With a proper choice of the norm for the test space, we prove robustness (uniform stability with respect to the diffusion parameter) and mesh-independence of the energy norm of the FE error for the 1D problem. With hp-adaptivity and a proper scaling of the norms for the test functions, we establish new limits for solving convection-dominated diffusion problems numerically: ε=10 -11 for 1D and ε=10 -7 for 2D problems. The adaptive process is fully automatic and starts with a mesh consisting of few elements only. © 2011 IMACS. Published by Elsevier B.V. All rights reserved.
Citation:
Demkowicz L, Gopalakrishnan J, Niemi AH (2012) A class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity. Applied Numerical Mathematics 62: 396–427. Available: http://dx.doi.org/10.1016/j.apnum.2011.09.002.
Publisher:
Elsevier BV
Journal:
Applied Numerical Mathematics
Issue Date:
Apr-2012
DOI:
10.1016/j.apnum.2011.09.002
Type:
Article
ISSN:
0168-9274
Sponsors:
Demkowicz was supported in part by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615], and by a research contract with Boeing. Gopalakrishnan was supported in part by the National Science Foundation under grant DMS-0713833. Niemi was supported in part by KAUST. We thank Bob Moser and David Young for encouragement and stimulating discussions on the project.
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Full metadata record

DC FieldValue Language
dc.contributor.authorDemkowicz, Leszeken
dc.contributor.authorGopalakrishnan, Jayen
dc.contributor.authorNiemi, Antti H.en
dc.date.accessioned2016-02-25T12:28:29Zen
dc.date.available2016-02-25T12:28:29Zen
dc.date.issued2012-04en
dc.identifier.citationDemkowicz L, Gopalakrishnan J, Niemi AH (2012) A class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity. Applied Numerical Mathematics 62: 396–427. Available: http://dx.doi.org/10.1016/j.apnum.2011.09.002.en
dc.identifier.issn0168-9274en
dc.identifier.doi10.1016/j.apnum.2011.09.002en
dc.identifier.urihttp://hdl.handle.net/10754/597230en
dc.description.abstractWe continue our theoretical and numerical study on the Discontinuous Petrov-Galerkin method with optimal test functions in context of 1D and 2D convection-dominated diffusion problems and hp-adaptivity. With a proper choice of the norm for the test space, we prove robustness (uniform stability with respect to the diffusion parameter) and mesh-independence of the energy norm of the FE error for the 1D problem. With hp-adaptivity and a proper scaling of the norms for the test functions, we establish new limits for solving convection-dominated diffusion problems numerically: ε=10 -11 for 1D and ε=10 -7 for 2D problems. The adaptive process is fully automatic and starts with a mesh consisting of few elements only. © 2011 IMACS. Published by Elsevier B.V. All rights reserved.en
dc.description.sponsorshipDemkowicz was supported in part by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615], and by a research contract with Boeing. Gopalakrishnan was supported in part by the National Science Foundation under grant DMS-0713833. Niemi was supported in part by KAUST. We thank Bob Moser and David Young for encouragement and stimulating discussions on the project.en
dc.publisherElsevier BVen
dc.subjectConvection-dominated diffusionen
dc.subjectDiscontinuous Petrov-Galerkinen
dc.subjecthp-Adaptivityen
dc.titleA class of discontinuous Petrov–Galerkin methods. Part III: Adaptivityen
dc.typeArticleen
dc.identifier.journalApplied Numerical Mathematicsen
dc.contributor.institutionUniversity of Texas at Austin, Austin, United Statesen
dc.contributor.institutionUniversity of Florida, Gainesville, United Statesen
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