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

In this article we propose fully discrete least-squares spectral element method for parabolic interface problems in R-2. 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 L-2(H-1) norm. Numerical results are presented to show the efficiency of the proposed method. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.