Convergence of Adaptive Mixed Interior Penalty Discontinuous Galerkin Methods for H(curl)-Elliptic Problems

TL;DR

This paper proves the convergence of an adaptive mixed interior penalty discontinuous Galerkin method for H(curl)-elliptic problems, introducing a new model, error analysis, and numerical validation.

Contribution

It develops a new mixed model for H(curl)-elliptic problems and establishes convergence of an adaptive discontinuous Galerkin method with error estimates.

Findings

Contraction of combined energy and scaled error indicator proven.

Numerical experiments confirm theoretical convergence.

New mixed model enhances solution accuracy.

Abstract

In this paper, we study the convergence of adaptive mixed interior penalty discontinuous Galerkin method for H(curl)-elliptic problems. We first get the mixed model of H(curl)-elliptic problem by introducing a new intermediate variable. Then we discuss the continuous variational problem and discrete variational problem, which based on interior penalty discontinuous Galerkin approximation. Next, we construct the corresponding posteriori error indicator, and prove the contraction of the summation of the energy error and the scaled error indicator. At last, we confirm and illustrate the theoretical result through some numerical experiments.