A New A Posteriori Error Estimate For The Interior Penalty Discontinuous Galerkin Method

In this paper,we develop the adaptive interior penalty discontinuous Galerkin method based on a new a posteriori error estimate for the second-order elliptic boundary-value problems.Firstly,we globally refine the current mesh Th to get the auxiliary mesh Th/2,then the numerical solution Uh of Th is interpolated on Tt/2 to derive uh/2,o-We obtain the approximation uh/2,m the finite element solution uh/2 by m(m?5)-time Gauss-Seidel iterations regarding uh/2,0 as the initial value.The new a posteriori error estimate is defined by the energy norm of error to uh/2,m and Uh.The efficiency and robustness of the presented adaptive method is illustrated by extensive numerical experiments.