Work

Study of a New Mixed Weak Galerkin Formulation for the Electric Field

Year: 2025

Type: article

Abstract: In this paper, we present a new mixed weak Galerkin FEM for Maxwell’s equations in the primary electrostatic field–Lagrange multiplier. Our numerical scheme is equipped with stable finite elements composed of polynomials of degree ℓ for the electrostatic variable and polynomials of degree 𝓁+1 for the Lagrange multiplier variable; the electrostatic field and the Lagrange multiplier variables are discontinuous. We demonstrate some error estimations that are optimal as a function of the mesh size and we study some numerical tests in a 2D domain. The numerical results perfectly confirm those shown theoretically.

Source: Mathematics

DOI: 10.3390/math13243926

Authors: Bader Saad Alshammari, Abdelhamid Zaghdani

Institutions: Northern Border University, Tunis University, ENSIT

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Northern Borders University