Analysis of a Weak Galerkin Mixed Formulation for Modified Maxwell’s Equations

Abdelhamid Zaghdani () and Abdelhalim Hasnaoui
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Abdelhamid Zaghdani: Faculty of Arts and Science, Northern Border University, Rafha P.O. Box 840, Saudi Arabia
Abdelhalim Hasnaoui: Faculty of Arts and Science, Northern Border University, Rafha P.O. Box 840, Saudi Arabia

Mathematics, 2024, vol. 12, issue 24, 1-9

Abstract: In this paper, we are interested in studying a mixed formulation of weak Galerkin type to approach the electric field and a Lagrange multiplier, which are solutions of a problem deriving from Maxwell’s equations. Our numerical scheme is formed with stable finite elements constructed of usual polynomials of degree k for the electric field and of degree k + 1 for the Lagrange multiplier; its consistency and well-posedness are shown. Some optimal error estimates are proven and tested numerically in a bounded subdomain of R 2 .

Keywords: weak Galerkin methods; mixed finite element methods; the Maxwell equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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