The adaptive immersed interface finite element method for elliptic and Maxwell interface problems

Authors:
Zhiming Chen;Yuanming Xiao;Linbo Zhang
Affiliations:
LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, People's Republic of China;Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China;LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, People's Republic of China
Venue:
Journal of Computational Physics
Year:
2009

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Abstract

We propose self-adaptive finite element methods with error control for solving elliptic and electromagnetic problems with discontinuous coefficients. The meshes in the methods do not need to fit the interfaces. New error indicators are introduced to control the error due to non-body-fitted meshes. Flexible h-adaptive strategies are developed, which can be systematically extended to a large class of interface problems. Extensive numerical experiments are performed to support the theoretical results and to show the competitive behavior of the adaptive algorithm even for interfaces involving corner or tip singularities.