A Discontinuous Galerkin Method for H(curl)-Elliptic Hemivariational Inequalities

TL;DR

This paper introduces a novel Discontinuous Galerkin method for solving H(curl)-elliptic hemivariational inequalities, with rigorous analysis and numerical validation of its convergence and stability.

Contribution

It develops an Interior Penalty Discontinuous Galerkin scheme specifically for H(curl)-elliptic hemivariational inequalities, including comprehensive theoretical analysis and numerical experiments.

Findings

The method achieves optimal convergence order under regularity assumptions.

Numerical results confirm the theoretical convergence and stability.

The scheme effectively solves the targeted hemivariational inequalities.

Abstract

In this paper, we develop a Discontinuous Galerkin (DG) method for solving H(curl)-elliptic hemivariational inequalities. By selecting an appropriate numerical flux, we construct an Interior Penalty Discontinuous Galerkin (IPDG) scheme. A comprehensive numerical analysis of the IPDG method is conducted, addressing key aspects such as consistency, boundedness, stability, and the existence, uniqueness, uniform boundedness of the numerical solutions. Building on these properties, we establish a priori error estimates, demonstrating the optimal convergence order of the numerical solutions under suitable solution regularity assumptions. Finally, a numerical example is presented to illustrate the theoretically predicted convergence order and to show the effectiveness of the proposed method.