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Fully discrete interior penalty discontinuous Galerkin methods for nonlinear parabolic equations

Authors

  • Lunji Song

    Corresponding author
    1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of China
    • School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of China
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Abstract

In this article, we investigate interior penalty discontinuous Galerkin (IPDG) methods for solving a class of two-dimensional nonlinear parabolic equations. For semi-discrete IPDG schemes on a quasi-uniform family of meshes, we obtain a priori bounds on solutions measured in the L2 norm and in the broken Sobolev norm. The fully discrete IPDG schemes considered are based on the approximation by forward Euler difference in time and broken Sobolev space. Under a restriction related to the mesh size and time step, an hp -version of an a priori l(L2) and l2(H1) error estimate is derived and numerical experiments are presented.© 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 288–311, 2012

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