Original title: Numerické řešení problému konvekce-difuse pomocí nespojité Galerkinovy metody
Translated title: Numerical solution of convection-diffusion problems by discontinuous Galerkin method
Authors: Vlasák, Miloslav ; Dolejší, Vít (advisor) ; Janovský, Vladimír (referee) ; Vejchodský, Tomáš (referee)
Document type: Doctoral theses
Year: 2010
Language: eng
Abstract: This work is concerned with the theoretical analysis of the discontinuous Galerkin finite element method. We use a discontinuous Galerkin formulation for a scalar convection-diffusion equation with nonlinear convective term. The resulting semidiscretized equations with symmetric (SIPG) or nonsymmetric (NIPG) diffusive term are then discretized in time by Backward Differential formulae (BDF), implicit Runge-Kutta methods and Time discontinuous Galerkin. All of these schemes are linearized by a suitable explicit extrapolations to avoid nonlinearity in the convective term. These final schemes are theoretically analyzed and error estimates are derived. We also present some superconvergence result for Time discontinuous Galerkin for nonsymmetric operator. Numerical experiments verify the theoretical results.

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/35442

Permalink: http://www.nusl.cz/ntk/nusl-379599


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Doctoral theses