Convergence of an adaptive discontinuous Galerkin method for the Biharmonic problem

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dc.contributor.advisorKreuzer, Christian
dc.contributor.authorDominicus, Alexander
dc.contributor.refereeGeorgoulis, Emmanuil H.
dc.date.accepted2020-07-17
dc.date.accessioned2021-02-25T14:07:34Z
dc.date.available2021-02-25T14:07:34Z
dc.date.issued2020
dc.description.abstractIn this thesis we develop a basic convergence result for an adaptive symmetric interior penalty discontinuous Galerkin discretisation for the Biharmonic problem which provides convergence without rates for arbitrary polynomial degree r≥2, all practically relevant marking strategies and all penalty parameters assuring coercivity of the method. We have to deal with the problem that the spaces consisting of piecewise polynomial functions may possibly contain no proper C^1-conforming subspace. This prevents from a straightforward generalisation of convergence results of adaptive discontinuous Galerkin methods for elliptic PDEs and requires the development of some new key technical tools. The convergence analysis is based on several embedding properties of (broken) Sobolev and BV spaces, and the construction of a suitable limit space of the non-conforming discrete spaces, created by the adaptive algorithm. Finally, the convergence result is validated through a number of numerical experiments.en
dc.identifier.urihttp://hdl.handle.net/2003/40054
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-21934
dc.language.isoende
dc.subjectAdaptive discontinuous Galerkin methodsen
dc.subjectSymmetric interior penalty methoden
dc.subjectConvergenceen
dc.subjectBiharmonic problemen
dc.subject.ddc510
dc.subject.rswkDiskontinuierliche Galerkin-Methodede
dc.subject.rswkAdaptives Verfahrende
dc.subject.rswkBipotentialgleichungde
dc.titleConvergence of an adaptive discontinuous Galerkin method for the Biharmonic problemen
dc.typeTextde
dc.type.publicationtypedoctoralThesisde
dcterms.accessRightsopen access
eldorado.secondarypublicationfalsede

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