Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems
Abstract
We deal with a posteriori error control of discontinuous Galerkin approximations for linear boundary value problems. The computational error is estimated in the framework of the Dual Weighted Residual method (DWR) for goal-oriented error estimation.
This requires to solve the primal as well as dual linear algebraic problems arising from the discretization. We focus on the control of the algebraic errors arising from iterative solutions of both algebraic systems.
Moreover, we present two different reconstructions techniques allowing an efficient evaluation of the error estimators. Finally, we propose a complex algorithm, which enables estimation of the error with respect to the goal functional and adaptation of the mesh in the close to optimal manner with respect to this quantity.
The performance of the algorithm is demonstrated by several numerical examples.