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2011-08-11Buch DOI: 10.18452/2782
Discontinuous Galerkin Finite Element Convergence for Incompressible Miscible Displacement Problems of Low Regularity
dc.contributor.authorBartels, Sören
dc.contributor.authorJensen, Max
dc.contributor.authorMüller, Rüdiger
dc.date.accessioned2017-06-15T18:17:09Z
dc.date.available2017-06-15T18:17:09Z
dc.date.created2011-08-11
dc.date.issued2011-08-11
dc.identifier.issn0863-0976
dc.identifier.urihttp://edoc.hu-berlin.de/18452/3434
dc.description.abstractIn this article we analyse the numerical approximation of incompressible miscible displacement problems with a combined mixed finite element and discontinuous Galerkin method under minimal regularity assumptions. The main result is that sequences of discrete solutions weakly accumulate at weak solutions of the continuous problem. In order to deal with the non-conformity of the method and to avoid overpenalisation of jumps across interelement boundaries, the careful construction of a reflexive subspace of the space of bounded variation, which compactly embeds into $L^2(\Omega)$, and of a lifting operator, which is compatible with the nonlinear diffusion coefficient, are required. An equivalent skew-symmetric formulation of the convection and reaction terms of the nonlinear partial differential equation allows to avoid flux limitation and nonetheless leads to an unconditionally stable and convergent numerical method. Numerical experiments underline the robustness of the proposed algorithm.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subject.ddc510 Mathematik
dc.titleDiscontinuous Galerkin Finite Element Convergence for Incompressible Miscible Displacement Problems of Low Regularity
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-100190697
dc.identifier.doihttp://dx.doi.org/10.18452/2782
local.edoc.container-titlePreprints aus dem Institut für Mathematik
local.edoc.pages20
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume2008
local.edoc.container-issue2
local.edoc.container-year2008
local.edoc.container-erstkatid2075199-0

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