Residual-Based Adaptivity and PWDG Methods for the Helmholtz Equation

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dc.citation.firstpageA1525en_US
dc.citation.issueNumber3en_US
dc.citation.journalTitleSIAM Journal on Scientific Computingen_US
dc.citation.lastpageA1553en_US
dc.citation.volumeNumber37en_US
dc.contributor.authorKapita, Shelveanen_US
dc.contributor.authorMonk, Peteren_US
dc.contributor.authorWarburton, Timothyen_US
dc.date.accessioned2017-06-05T19:27:05Zen_US
dc.date.available2017-06-05T19:27:05Zen_US
dc.date.issued2015en_US
dc.description.abstractWe present a study of two residual a posteriori error indicators for the plane wave discontinuous Galerkin (PWDG) method for the Helmholtz equation. In particular, we study the $h$-version of PWDG in which the number of plane wave directions per element is kept fixed. First, we use a slight modification of the appropriate a priori analysis to determine a residual indicator. Numerical tests show that this is reliable but pessimistic in that the ratio between the true error and the indicator increases as the mesh is refined. We therefore introduce a new analysis based on the observation that sufficiently many plane waves can approximate piecewise linear functions as the mesh is refined. Numerical results demonstrate an improvement in the efficiency of the indicators.en_US
dc.identifier.citationKapita, Shelvean, Monk, Peter and Warburton, Timothy. "Residual-Based Adaptivity and PWDG Methods for the Helmholtz Equation." <i>SIAM Journal on Scientific Computing,</i> 37, no. 3 (2015) Society for Industrial and Applied Mathematics: A1525-A1553. http://dx.doi.org/10.1137/140967696.en_US
dc.identifier.doihttp://dx.doi.org/10.1137/140967696en_US
dc.identifier.urihttps://hdl.handle.net/1911/94788en_US
dc.language.isoengen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.titleResidual-Based Adaptivity and PWDG Methods for the Helmholtz Equationen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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