Adaptive direct discontinuous Galerkin method for elliptic equations.

In this paper, adaptive direct discontinuous Galerkin method for second order elliptic equations is studied in two dimensional. A numerical flux with general weighted averages and proper weights for interface problems is introduced. In addition to the optimal a priori error estimator, we propose a residual-type a posteriori error estimator. The global upper bound and local lower bound for the error in DG norm are established. Several numerical examples are carried out to confirm the reliability and efficiency of the proposed error estimator and the corresponding adaptive direct discontinuous Galerkin method. [ABSTRACT FROM AUTHOR]