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Extension Of The High-Order Space-Time Discontinuous Galerkin Cell Vertex Scheme To Solve Time Dependent Diffusion Equations

Published online by Cambridge University Press:  20 August 2015

Shuangzhang Tu ,
Gordon W. Skelton  and
Qing Pang
Shuangzhang Tu*
Affiliation:
Department of Computer Engineering, Jackson State University, Jackson, MS 39217, USA
Gordon W. Skelton*
Affiliation:
Department of Computer Engineering, Jackson State University, Jackson, MS 39217, USA
Qing Pang*
Affiliation:
Department of Computer Engineering, Jackson State University, Jackson, MS 39217, USA
*
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
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Abstract

In this paper, the high-order space-time discontinuous Galerkin cell vertex scheme (DG-CVS) developed by the authors for hyperbolic conservation laws is extended for time dependent diffusion equations. In the extension, the treatment of the diffusive flux is exactly the same as that for the advective flux. Thanks to the Riemann-solver-free and reconstruction-free features of DG-CVS, both the advective flux and the diffusive flux are evaluated using continuous information across the cell interface. As a result, the resulting formulation with diffusive fluxes present is still consistent and does not need any extra ad hoc techniques to cure the common “variational crime” problem when traditional DG methods are applied to diffusion problems. For this reason, DG-CVS is conceptually simpler than other existing DG-typed methods.

Keywords

65M9976M25High-order methodspace-time methoddiscontinuous Galerkin (DG) methodcell-vertex scheme (CVS)diffusion equations
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 5 , May 2012 , pp. 1503 - 1524
Copyright
Copyright © Global Science Press Limited 2012

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