Abstract 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.

中文翻译：

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抛物线界面问题的全离散最小二乘谱元法

摘要 在本文中，我们针对 R 2 中的抛物线界面问题提出了完全离散的最小二乘谱元方法。Crank-Nicolson 方案在时间上使用，而在空间方向上使用更高阶的光谱元素。该方法基于 Kishore Kumar 和 Naga Raju (2012) 提出的非一致性光谱元素方法。所提出的方法是最小二乘谱元法。不合格的高阶光谱元素已被使用。在最小化函数中强制执行解中的跳跃及其跨界面的法向导数（以适当的 Sobolev 范数）。该方法在时间上是二阶精确的，在空间方向上是指数级精确的，p - 版本在 L 2 (H 1 ) 范数中。数值结果显示了所提出方法的有效性。