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Convergence of a Second-Order Linearized BDF–IPDG for Nonlinear Parabolic Equations with Discontinuous Coefficients

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Abstract

We study the anti-symmetric interior over-penalized discontinuous Galerkin finite element methods for solving nonlinear parabolic interface problems with second-order backward difference formula for the time discretization, where the diffusion coefficient depends on the unknown solution and is discontinuous across the interface. We present optimal-order error estimates for the finite element solution based on piecewise regularity of the solution.

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Acknowledgments

We are grateful to the anonymous referees for the valuable comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, People’s Republic of China

    Lunji Song

  2. Center for Visual Cognitive Computation and its Application, Department of Mathematics, College of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, Jiangsu, People’s Republic of China

    Chaoxia Yang

Authors
  1. Lunji Song
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  2. Chaoxia Yang
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Corresponding author

Correspondence to Chaoxia Yang.

Additional information

Lunji Song was partially supported by NSFC (Grant No. 11101196) and by the Natural Science Foundation of Gansu Province, China (Grant No. 145RJZA046).

Chaoxia Yang was supported in part by NSFC (Grant No. 11401587) and the Jiangsu Overseas Research & Training Program for University Prominent Young & Middle-aged Teachers and Presidents.

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Song, L., Yang, C. Convergence of a Second-Order Linearized BDF–IPDG for Nonlinear Parabolic Equations with Discontinuous Coefficients. J Sci Comput 70, 662–685 (2017). https://doi.org/10.1007/s10915-016-0261-2

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  • DOI: https://doi.org/10.1007/s10915-016-0261-2

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