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

University of Arkansas at Little Rock
University of Delaware

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

1 Scopus citations

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
Pages (from-to)	949-960
Number of pages	12
Journal	Computational Methods in Applied Mathematics
Volume	25
Issue number	4
DOIs	https://doi.org/10.1515/cmam-2024-0144
State	Published - 1 Oct 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",

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AU - Nie, Yufeng

AU - Ye, Xiu

AU - Zhang, Shangyou

PY - 2025/10/1

Y1 - 2025/10/1

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

UR - https://www.scopus.com/pages/publications/85217968143

U2 - 10.1515/cmam-2024-0144

DO - 10.1515/cmam-2024-0144

M3 - 文章

AN - SCOPUS:85217968143

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SP - 949

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JO - Computational Methods in Applied Mathematics

JF - Computational Methods in Applied Mathematics

IS - 4

ER -

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

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Keywords

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