HDG methods for elastodynamics

dc.contributor.authorHungria, Allan
dc.contributor.authorPrada, Daniele
dc.contributor.authorSayas, Francisco-Javier
dc.contributor.departmentMathematical Sciences, School of Scienceen_US
dc.date.accessioned2018-04-12T13:53:59Z
dc.date.available2018-04-12T13:53:59Z
dc.date.issued2017-12
dc.description.abstractWe derive and analyze a hybridizable discontinuous Galerkin (HDG) method for approximating weak solutions to the equations of time-harmonic linear elasticity on a bounded Lipschitz domain in three dimensions. The real symmetry of the stress tensor is strongly enforced and its coefficients as well as those of the displacement vector field are approximated simultaneously at optimal convergence with respect to the choice of approximating spaces, wavenumber, and mesh size. Sufficient conditions are given so that the system is indeed transferable onto a global hybrid variable that, for larger polynomial degrees, may be approximated via a smaller-dimensional space than the original variables. We construct several variants of this method and discuss their advantages and disadvantages, and give a systematic approach to the error analysis for these methods. We touch briefly on the application of this error analysis to the time-dependent problem, and finally, we examine two different implementations of the method over various polynomial degrees and numerically demonstrate the convergence properties proven herein.en_US
dc.eprint.versionAuthor's manuscripten_US
dc.identifier.citationHungria, A., Prada, D., & Sayas, F.-J. (2017). HDG methods for elastodynamics. Computers & Mathematics with Applications, 74(11), 2671–2690. https://doi.org/10.1016/j.camwa.2017.08.016en_US
dc.identifier.urihttps://hdl.handle.net/1805/15836
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.relation.isversionof10.1016/j.camwa.2017.08.016en_US
dc.relation.journalComputers & Mathematics with Applicationsen_US
dc.rightsPublisher Policyen_US
dc.sourceArXiven_US
dc.subjecthybridizable DG methodsen_US
dc.subjectelastic wave equationen_US
dc.subjecttime-harmonic solutionsen_US
dc.titleHDG methods for elastodynamicsen_US
dc.typeArticleen_US
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