Superconvergence of immersed finite element methods for interface problems |
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Authors: | Waixiang Cao Xu Zhang Zhimin Zhang |
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Institution: | 1.Beijing Computational Science Research Center,Beijing,China;2.Department of Mathematics and Statistics,Mississippi State University,Mississippi State,USA;3.Department of Mathematics,Wayne State University,Detroit,USA |
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Abstract: | In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the solution, classical superconvergence phenomenon for finite element methods disappears unless the discontinuity of the coefficient is resolved by partition. We show that immersed finite element solutions inherit all desired superconvergence properties from standard finite element methods without requiring the mesh to be aligned with the interface. In particular, on interface elements, superconvergence occurs at roots of generalized orthogonal polynomials that satisfy both orthogonality and interface jump conditions. |
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