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Fully discrete least-squares spectral element method for parabolic interface problems

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  • Kishore Kumar, N.
  • Biswas, Pankaj

Abstract

In this article we propose fully discrete least-squares spectral element method for parabolic interface problems in R2. Crank–Nicolson scheme is used in time and higher order spectral elements are used in the spatial direction. This method is based on the nonconforming spectral element method proposed in Kishore Kumar and Naga Raju (2012). The proposed method is least-squares spectral element method. Nonconforming higher order spectral elements have been used. The jump in the solution and its normal derivative across the interface are enforced (in an appropriate Sobolev norm) in the minimizing functional. The method is second order accurate in time and exponentially accurate in spatial direction with p−version in L2(H1) norm. Numerical results are presented to show the efficiency of the proposed method.

Suggested Citation

  • Kishore Kumar, N. & Biswas, Pankaj, 2021. "Fully discrete least-squares spectral element method for parabolic interface problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 364-379.
    • Handle: RePEc:eee:matcom:v:181:y:2021:i:c:p:364-379
    DOI: 10.1016/j.matcom.2020.10.001
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    References listed on IDEAS

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    1. Li, Chuan & Zhao, Shan, 2017. "A matched Peaceman–Rachford ADI method for solving parabolic interface problems," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 28-44.
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