Year: 2023
Author: Yan Chen, Ruo Li, Qicheng Liu
Annals of Applied Mathematics, Vol. 39 (2023), Iss. 2 : pp. 149–180
Abstract
We present an arbitrary order discontinuous Galerkin finite element method for solving the biharmonic interface problem on the unfitted mesh. The approximation space is constructed by a patch reconstruction process with at most one degrees of freedom per element. The discrete problem is based on the symmetric interior penalty method and the jump conditions are weakly imposed by the Nitsche’s technique. The $C^2$-smooth interface is allowed to intersect elements in a very general fashion and the stability near the interface is naturally ensured by the patch reconstruction. We prove the optimal a priori error estimate under the energy norm and the $L^2$ norm. Numerical results are provided to verify the theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2023-0011
Annals of Applied Mathematics, Vol. 39 (2023), Iss. 2 : pp. 149–180
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Biharmonic interface problem patch reconstruction discontinuous Galerkin method.