Název:
Numerické řešení problému konvekce-difuse pomocí nespojité Galerkinovy metody
Překlad názvu:
Numerical solution of convection-diffusion problems by discontinuous Galerkin method
Autoři:
Vlasák, Miloslav ; Dolejší, Vít (vedoucí práce) ; Janovský, Vladimír (oponent) ; Vejchodský, Tomáš (oponent) Typ dokumentu: Disertační práce
Rok:
2010
Jazyk:
eng
Abstrakt: 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.