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Interior penalty discontinuous Galerkin methods with implicit time-integration techniques for nonlinear parabolic equations

Authors

  • Lunji Song,

    Corresponding author
    1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of China
    2. Beijing Computational Science Research Center, Beijing 100084, People's Republic of China
    • School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of China
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  • Gung-Min Gie,

    1. Department of Mathematics, University of California Riverside, Riverside, California 92521
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  • Ming-Cheng Shiue

    1. Department of Applied Mathematics, National Chiao Tung University, Taiwan
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  • This work was partly done when the first author worked as a vistor at Beijing Computational Science Research Center (CSRC).

Abstract

We prove existence and numerical stability of numerical solutions of three fully discrete interior penalty discontinuous Galerkin methods for solving nonlinear parabolic equations. Under some appropriate regularity conditions, we give the l2(H1) and l(L2) error estimates of the fully discrete symmetric interior penalty discontinuous Galerkin–scheme with the implicit θ -schemes in time, which include backward Euler and Crank–Nicolson finite difference approximations. Our estimates are optimal with respect to the mesh size h. The theoretical results are confirmed by some numerical experiments. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013

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