A Posteriori Error Analysis

For linear and non-linear partial differential equations we investigate mesh-based methods ranging from continuous FEM (finite element) to DG (discontinuous Galerkin) methods. One main goal is to provide a posteriori error estimators, i.e., error bounds that can be explicitly computed from the numerical solution. These estimators provide error control as well as important information for mesh adaptation. One approach for deriving such estimators are relative-energy type stability estimates that are combined with conforming reconstructions of numerical solutions. Another approach uses dual weighted residuals that account for goal functionals of particular interest by solving adjoint problems.