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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Communicated by: Jan Hesthaven
This work is supported in part by the China Postdoctoral Science Foundation 2015M570026, and the National Natural Science Foundation of China (NSFC) under grants No. 91430216, 11471031, 11501026, and the US National Science Foundation (NSF) through grant DMS-1419040.
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Cao, W., Zhang, X. & Zhang, Z. Superconvergence of immersed finite element methods for interface problems. Adv Comput Math 43, 795–821 (2017). https://doi.org/10.1007/s10444-016-9507-7
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DOI: https://doi.org/10.1007/s10444-016-9507-7