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weighted interior penalty Methodwith Semi-Implicit Integration Factor Method for Non-Equilibrium Radiation Diffusion Equation

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Communications in Computational Physics 2013年第10期14卷 1287-1303页

作者： Rongpei Zhang Xijun Yu Jiang Zhu Abimael F.D.Loula Xia Cui School of Sciences Liaoning ShiHua UniversityFushun 113001China Laboratory of Computational Physics Institute of Applied Physics and ComputationalMathematicsBeijing 100088China Laborat´orio Nacional de Computa¸cao Cient´ıfica MCTIAvenida Get´ulio Vargas33325651-075 Petr´opolisRJBrazil

weighted interior penalty discontinuous Galerkin method is developed to solve the two-dimensional non-equilibrium radiation diffusion equation on unstructured *** are three weights including the arithmetic,the harmonic,and the geometric weight in the weighted discontinuous Galerkin *** the time discretization,we treat the nonlinear diffusion coefficients explicitly,and apply the semiimplicit integration factormethod to the nonlinear ordinary differential equations arising from discontinuous Galerkin spatial *** semi-implicit integration factor method can not only avoid severe timestep limits,but also takes advantage of the local property of DG methods by which small sized nonlinear algebraic systems are solved element by element with the exact Newton iteration *** results are presented to demonstrate the validity of discontinuous Galerkin method for high nonlinear and tightly coupled radiation diffusion equation.

关键词： Discontinuous Galerkin weighted interior penalty semi-implicit integration factor non-equilibrium radiation diffusion

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A POSTERIORI ENERGY-NORM ERROR ESTIMATES FOR ADVECTION-DIFFUSION EQUATIONS APPROXIMATED BY weighted interior penalty METHODS

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Journal of Computational Mathematics 2008年第4期26卷 488-510页

作者： Alexandre Ern AnnetteF.Stephansen Université Paris-Est CermicsEcole des Ponts6 et 8 avenue Blaise PascalChamps sur Marne77455 Marne la Vallée Cedex 2France Université Paris-Est CermicsEcole des Ponts6 et 8 avenue Blaise PascalChamps sur Marne77455 Marne la Vallée Cedex 2France AndraParc de la Croix-Blanche1-7 rue Jean Monnet92298 Ch■tenay-Malabry cedexFrance

We propose and analyze a posteriori energy-norm error estimates for weighted interior penalty discontinuous Galerkin approximations of advection-diffusion-reaction equations with heterogeneous and anisotropic diffusion. The weights, which play a key role in the analysis, depend on the diffusion tensor and are used to formulate the consistency terms in the discontinuous Galerkin method. The error upper bounds, in which all the constants are specified, consist of three terms： a residual estimator which depends only on the elementwise fluctuation of the discrete solution residual, a diffusive flux estimator where the weights used in the method enter explicitly, and a non-conforming estimator which is nonzero because of the use of discontinuous finite element spaces. The three estimators can be bounded locally by the approximation error. A particular attention is given to the dependency on problem parameters of the constants in the local lower error bounds. For moderate advection, it is shown that full robustness with respect to diffusion heterogeneities is achieved owing to the specific design of the weights in the discontinuous Galerkin method, while diffusion anisotropies remain purely local and impact the constants through the square root of the condition number of the diffusion tensor. For dominant advection, it is shown, in the spirit of previous work by Verfiirth on continuous finite elements, that the local lower error bounds can be written with constants involving a cut-off for the ratio of local mesh size to the reciprocal of the square root of the lowest local eignevalue of the diffusion tensor.

关键词： Discontinuous Galerkin weighted interior penalty A posteriori error estimate,Heterogeneous diffusion Advection-diffusion.

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