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

Author

Listed:
  • Abdelhamid Zaghdani

    (Faculty of Arts and Science, Northern Border University, Rafha P.O. Box 840, Saudi Arabia
    These authors contributed equally to this work.)

  • Abdelhalim Hasnaoui

    (Faculty of Arts and Science, Northern Border University, Rafha P.O. Box 840, Saudi Arabia
    These authors contributed equally to this work.)

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 .

Suggested Citation

  • Abdelhamid Zaghdani & Abdelhalim Hasnaoui, 2024. "Analysis of a Weak Galerkin Mixed Formulation for Modified Maxwell’s Equations," Mathematics, MDPI, vol. 12(24), pages 1-9, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3901-:d:1541424
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