A Potential-Robust WG Finite Element Method for the Maxwell Equations on Tetrahedral Meshes

Yufeng Nie; Xiu Ye; Shangyou Zhang

doi:10.1515/cmam-2024-0144

A Potential-Robust WG Finite Element Method for the Maxwell Equations on Tetrahedral Meshes

Yufeng Nie, Xiu Ye, Shangyou Zhang

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

A potential-robust WG (weak Galerkin) method is introduced for the Maxwell equations. We obtain potential/magnetic-permeability independent error estimates. Optimal-order convergence rates are proved in both the energy norm and the L² norm. Numerical examples verify the theory.

Original language	English
Journal	Computational Methods in Applied Mathematics
DOIs	https://doi.org/10.1515/cmam-2024-0144
State	Accepted/In press - 2025

Keywords

Finite Element
Maxwell Equations
Potential Robust
Tetrahedral Meshes
Weak Galerkin

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10.1515/cmam-2024-0144

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title = "A Potential-Robust WG Finite Element Method for the Maxwell Equations on Tetrahedral Meshes",

abstract = "A potential-robust WG (weak Galerkin) method is introduced for the Maxwell equations. We obtain potential/magnetic-permeability independent error estimates. Optimal-order convergence rates are proved in both the energy norm and the L2 norm. Numerical examples verify the theory.",

keywords = "Finite Element, Maxwell Equations, Potential Robust, Tetrahedral Meshes, Weak Galerkin",

author = "Yufeng Nie and Xiu Ye and Shangyou Zhang",

note = "Publisher Copyright: {\textcopyright} 2025 Walter de Gruyter GmbH, Berlin/Boston 2025.",

year = "2025",

doi = "10.1515/cmam-2024-0144",

language = "英语",

journal = "Computational Methods in Applied Mathematics",

issn = "1609-4840",

publisher = "Walter de Gruyter GmbH",

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AU - Nie, Yufeng

AU - Ye, Xiu

AU - Zhang, Shangyou

PY - 2025

Y1 - 2025

N2 - A potential-robust WG (weak Galerkin) method is introduced for the Maxwell equations. We obtain potential/magnetic-permeability independent error estimates. Optimal-order convergence rates are proved in both the energy norm and the L2 norm. Numerical examples verify the theory.

AB - A potential-robust WG (weak Galerkin) method is introduced for the Maxwell equations. We obtain potential/magnetic-permeability independent error estimates. Optimal-order convergence rates are proved in both the energy norm and the L2 norm. Numerical examples verify the theory.

KW - Finite Element

KW - Maxwell Equations

KW - Potential Robust

KW - Tetrahedral Meshes

KW - Weak Galerkin

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U2 - 10.1515/cmam-2024-0144

DO - 10.1515/cmam-2024-0144

M3 - 文章

AN - SCOPUS:85217968143

SN - 1609-4840

JO - Computational Methods in Applied Mathematics

JF - Computational Methods in Applied Mathematics

ER -

A Potential-Robust WG Finite Element Method for the Maxwell Equations on Tetrahedral Meshes

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