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Journal of Engineering Mathematics
Published in:

01-08-2023

A new Petrov–Galerkin immersed finite element method for elliptic interface problems with non-homogeneous jump conditions

Authors: Zhongliang Tang, Yu Zheng, Liqun Wang, Quanxiang Wang

Published in: Journal of Engineering Mathematics | Issue 1/2023

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Abstract

The article introduces a new Petrov–Galerkin immersed finite element method for solving elliptic interface problems with non-homogeneous jump conditions. It discusses the challenges of solving such problems analytically due to the poor global smoothness of the solution. The method is classified into two main categories: interface-fitted meshes and interface-unfitted meshes. The main contribution of the paper is the construction of piecewise IFE functions for three-dimensional problems that can satisfy the non-homogeneous jump conditions in an approximate sense. The method is simple, can be processed in parallel, and can be easily extended to solve three-dimensional elasticity interface problems and band structure computation of phononic crystals. Extensive numerical examples demonstrate the effectiveness and accuracy of the method, achieving nearly second-order accuracy in the and norm.
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previous article Existence of entropy weak solutions for 1D non-local traffic models with space-discontinuous flux
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Metadata
Title
A new Petrov–Galerkin immersed finite element method for elliptic interface problems with non-homogeneous jump conditions
Authors
Zhongliang Tang
Yu Zheng
Liqun Wang
Quanxiang Wang
Publication date
01-08-2023
Publisher
Springer Netherlands
Published in
Journal of Engineering Mathematics / Issue 1/2023
Print ISSN: 0022-0833
Electronic ISSN: 1573-2703
DOI
https://doi.org/10.1007/s10665-023-10286-3

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