A posteriori error estimates and adaptive mesh refinement for the Stokes–Brinkman problem

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dc.contributor.authorWilliamson, Kevin
dc.contributor.authorBurda, Pavel
dc.contributor.authorSousedik, Bedrich
dc.date.accessioned2018-10-23T13:42:27Z
dc.date.available2018-10-23T13:42:27Z
dc.date.issued2019-6-6
dc.description.abstractThe Stokes–Brinkman equations model flow in heterogeneous porous media by combining the Stokes and Darcy models of flow into a single system of equations. With suitable parameters, the equations can model either flow without detailed knowledge of the interface between the two regions. Thus, the Stokes–Brinkman equations provide an alternative to coupled Darcy–Stokes models. After a brief review of the Stokes–Brinkman problem and its discretization using Taylor–Hood finite elements, we present a residual-based a posteriori error estimate and use it to drive an adaptive mesh refinement process. We compare several strategies for the mesh refinement, and demonstrate its effectiveness by numerical experiments in both 2D and 3D.en_US
dc.description.sponsorshipSupported by the U.S. National Science Foundation under grant DMS1521563.en_US
dc.description.urihttps://www.sciencedirect.com/science/article/pii/S0378475419301910en_US
dc.format.extent17 pagesen_US
dc.genrejournal articlesen_US
dc.genrepreprints
dc.identifierdoi:10.13016/M24B2X839
dc.identifier.citationWilliamson, Kevin, Pavel Burda, and Bedřich Sousedík. “A Posteriori Error Estimates and Adaptive Mesh Refinement for the Stokes–Brinkman Problem.” Mathematics and Computers in Simulation 166 (December 1, 2019): 266–82. https://doi.org/10.1016/j.matcom.2019.05.015.
dc.identifier.urihttps://doi.org/10.1016/j.matcom.2019.05.015
dc.identifier.urihttp://hdl.handle.net/11603/11647
dc.language.isoen_USen_US
dc.publisherElsevier
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics Department Collection
dc.relation.ispartofUMBC Faculty Collection
dc.relation.ispartofUMBC Student Collection
dc.rightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
dc.subjecta posteriori error estimatesen_US
dc.subjectStokes–Brinkman problemen_US
dc.subjectadaptive mesh refinementen_US
dc.titleA posteriori error estimates and adaptive mesh refinement for the Stokes–Brinkman problemen_US
dc.typeTexten_US
dcterms.creatorhttps://orcid.org/0000-0002-8053-8956

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