Residual-based a posteriori error estimation for immersed finite element methods

2019/10/17 by Cuiyu He, Xu Zhang, He, Cuiyu +1 · 1 citation
Engineering · #35R05 #65N15 #65N30 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1910.07711

openalex publication_date 2019/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce and analyze the residual-based a posteriori error estimation of the partially penalized immersed finite element method for solving elliptic interface problems. The immersed finite element method can be naturally utilized on interface-unfitted meshes. Our a posteriori error estimate is proved to be both reliable and efficient with reliability constant independent of the location of the interface. Numerical results indicate that the efficiency constant is independent of the interface location and that the error estimation is robust with respect to the coefficient contrast.

Citations

• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• A finite element method for crack growth without remeshing

Cited by

• Elliptic Interface Problem approximated by CutFEM: II. A posteriori error analysis based on equilibrated fluxes

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