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

dc.contributor.authorDemkowicz, Leszek
dc.contributor.authorGopalakrishnan, Jay
dc.contributor.authorNiemi, Antti H.
dc.contributor.institutionUniversity of Texas at Austin, Austin, United States
dc.contributor.institutionUniversity of Florida, Gainesville, United States
dc.date.accessioned2016-02-25T12:28:29Z
dc.date.available2016-02-25T12:28:29Z
dc.date.issued2012-04
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.
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.
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.
dc.identifier.doi10.1016/j.apnum.2011.09.002
dc.identifier.issn0168-9274
dc.identifier.journalApplied Numerical Mathematics
dc.identifier.urihttp://hdl.handle.net/10754/597230
dc.publisherElsevier BV
dc.subjectConvection-dominated diffusion
dc.subjectDiscontinuous Petrov-Galerkin
dc.subjecthp-Adaptivity
dc.titleA class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity
dc.typeArticle
display.details.left<span><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Demkowicz, Leszek,equals">Demkowicz, Leszek</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Gopalakrishnan, Jay,equals">Gopalakrishnan, Jay</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Niemi, Antti H.,equals">Niemi, Antti H.</a><br><br><h5>Date</h5>2012-04</span>
display.details.right<span><h5>Abstract</h5>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.<br><br><h5>Citation</h5>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.<br><br><h5>Acknowledgements</h5>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.<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=Elsevier BV,equals">Elsevier BV</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=Applied Numerical Mathematics,equals">Applied Numerical Mathematics</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1016/j.apnum.2011.09.002">10.1016/j.apnum.2011.09.002</a></span>
orcid.authorDemkowicz, Leszek
orcid.authorGopalakrishnan, Jay
orcid.authorNiemi, Antti H.
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