An Arbitrary Order Mixed Finite Element Method with Boundary Value Correction for the Darcy Flow on Curved Domains
Year: 2025
Author: Yongli Hou, Yanqiu Wang
Communications in Computational Physics, Vol. 37 (2025), Iss. 5 : pp. 1227–1249
Abstract
We propose a boundary value correction method for the Brezzi-Douglas-Marini mixed finite element discretization of the Darcy flow with non-homogeneous Neumann boundary condition on 2D curved domains. The discretization is defined on a body-fitted triangular mesh, i.e. the boundary nodes of the mesh lie on the curved physical boundary. However, the boundary edges of the triangular mesh, which are straight, may not coincide with the curved physical boundary. A boundary value correction technique is then designed to transform the Neumann boundary condition from the physical boundary to the boundary of the triangular mesh. One advantage of the boundary value correction method is that it avoids using curved mesh elements and thus reduces the complexity of implementation. We prove that the proposed method reaches optimal convergence for arbitrary order discretizations. Supporting numerical results are presented.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2024-0317
Communications in Computational Physics, Vol. 37 (2025), Iss. 5 : pp. 1227–1249
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Mixed finite element method Neumann boundary condition curved domain boundary value correction method.