Convergence of adaptive mixed interior penalty discontinuous Galerkin methods for H(curl)-elliptic problems

Abstract

In this paper, we study the convergence of adaptive mixed interior penalty discontinuous Galerkin method for $H\left(curl\right)$-elliptic problems. We first get the mixed model of $H\left(curl\right)$-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.