Error Analysis of Symmetric Linear/Bilinear Partially Penalized Immersed Finite Element Methods for Helmholtz Interface Problems
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This article presents an error analysis of the symmetric linear/bilinear partially penalized immersed finite element (PPIFE) methods for interface problems of Helmholtz equations. Under the assumption that the exact solution possesses a usual piecewise H^2 regularity, the optimal error bounds for the PPIFE solutions are derived in an energy norm and the usual L^2 norm provided that the mesh size is sufficiently small. A numerical example is conducted to validate the theoretical conclusions.
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