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A Family of Two-Grid Partially Penalized Immersed Finite Element Methods for Semi-linear Parabolic Interface Problems

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Abstract

In this paper, we present a family of two-grid algorithms for semi-linear parabolic interface problems based on Partially penalized immersed finite element discretizations. Optimal a priori error estimates are derived both in the energy norm and \(L^2\) norm, under the standard piecewise \(H^2\) regularity assumption for the exact solution. For the nonlinear right hand side, we investigate two-grid methods base on Newton method. The efficiency of the two-grid methods is confirmed theoretically and numerically.

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, 411105, China

    Yang Wang, Yunqing Huang & Huaming Yi

  2. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    Yanping Chen

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This work is supported by National Natural Science Foundation of China (41974133, 11971410) and the State Key Program of National Natural Science Foundation of China (11931003) and Project for Hunan National Applied Mathematics Center of Hunan Provincial Science and Technology Department (2020ZYT003) and Postgraduate Scientific Research Innovation Project of Xiangtan University (XDCX2021B109)

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Wang, Y., Chen, Y., Huang, Y. et al. A Family of Two-Grid Partially Penalized Immersed Finite Element Methods for Semi-linear Parabolic Interface Problems. J Sci Comput 88, 80 (2021). https://doi.org/10.1007/s10915-021-01575-z

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