Time Implicit High-Order Discontinuous Galerkin Method with Reduced Evaluation Cost

Authors:
Florent Renac;Claude Marmignon;Frédéric Coquel
Affiliations:
florent.renac@onera.fr and claude.marmignon@onera.fr;-;frederic.coquel@cmap.polytechnique.fr
Venue:
SIAM Journal on Scientific Computing
Year:
2012

Citing 15
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Abstract

An efficient and robust time integration procedure for a high-order discontinuous Galerkin method is introduced for solving nonlinear second-order partial differential equations. The time discretization is based on an explicit formulation for the hyperbolic term and an implicit formulation for the parabolic term. The procedure uses an iterative algorithm with reduced evaluation cost. The size of the linear system to be solved is greatly reduced thanks to partial uncoupling in space between low-order and high-order degrees of freedom. Numerical examples are presented for the nonlinear convection-diffusion equation in one and two dimensions including steady and unsteady flow problems. The performance of the present method is investigated in terms of CPU time and compared to a fully implicit method. A von Neumann stability analysis is carried out in order to determine the stability and damping properties of the method. Besides a fairly reduced CPU effort, numerical results demonstrate better convergence properties of the present algorithm when compared to the fully implicit method.