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Journal of Scientific Computing

Erschienen in:

01.02.2013

A New Nonsymmetric Discontinuous Galerkin Method for Time Dependent Convection Diffusion Equations

verfasst von: Jue Yan

Erschienen in: Journal of Scientific Computing | Ausgabe 2-3/2013

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Abstract

We propose a discontinuous Galerkin finite element method for convection diffusion equations that involves a new methodology handling the diffusion term. Test function derivative numerical flux term is introduced in the scheme formulation to balance the solution derivative numerical flux term. The scheme has a nonsymmetric structure. For general nonlinear diffusion equations, nonlinear stability of the numerical solution is obtained. Optimal kth order error estimate under energy norm is proved for linear diffusion problems with piecewise P ^k polynomial approximations. Numerical examples under one-dimensional and two-dimensional settings are carried out. Optimal (k+1)th order of accuracy with P ^k polynomial approximations is obtained on uniform and nonuniform meshes. Compared to the Baumann-Oden method and the NIPG method, the optimal convergence is recovered for even order P ^k polynomial approximations.

Vorheriger Artikel High Order Well-Balanced WENO Scheme for the Gas Dynamics Equations Under Gravitational Fields

Nächster Artikel Error Forgetting of Bregman Iteration

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Titel: A New Nonsymmetric Discontinuous Galerkin Method for Time Dependent Convection Diffusion Equations
verfasst von: Jue Yan
Publikationsdatum: 01.02.2013
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2-3/2013
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-012-9637-0

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