What question did this study set out to answer?

December 9, 2025Open Access

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

Key Points

This research aims to develop a new mixed weak Galerkin FEM for Maxwell's equations in the electrostatic field.
Introduced a mixed weak Galerkin FEM framework for solving Maxwell’s equations.
Used stable finite elements with polynomials of degree ℓ for the electrostatic variable.
Performed numerical tests in a 2D domain to validate theoretical results.
Achieved optimal error estimations as a function of mesh size.
Confirmed numerical results align with theoretical predictions.

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.

Read Full Paperexternally

Mark Helpful

Bookmark

Relay

View Full Paper