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

N. Kishore Kumar and Pankaj Biswas

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 181, issue C, 364-379

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.

Keywords: Spectral element; Nonconforming; Parabolic interface problem; Crank–Nicolson scheme; Least-squares; Timestep (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:181:y:2021:i:c:p:364-379

DOI: 10.1016/j.matcom.2020.10.001

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