Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection–diffusion–reaction problems

Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems

We propose and study a posteriori error estimates for convection–diffusion–reaction problems with inhomogeneous and anisotropic diffusion approximated by weighted interiorpenalty discontinuous Galerkin methods. Our twofold objective is to derive estimates without undetermined constants and to analyze carefully the robustness of the estimates in singularly perturbed regimes due to dominant conve...

Guaranteed a Posteriori Error Estimates for Viscous Flow Problems

In the talk, we discuss a posteriori error estimates for elliptic and parabolic viscous flow problems and give an overview of the results obtained in this field with the help of a new (functional) approach that was earlier applied to many problems in mathematical physics. This method provides guaranteed and computable error bounds that do not involve mesh dependent constants and are valid for a...

A Posteriori Error Estimates and Mesh Adaptation Strategy for Discontinuous Galerkin Methods Applied to Diffusion Problems

A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems

Several a posteriori error estimators are introduced and analyzed for a discontinuous Galerkin formulation of a model second-order elliptic problem. In addition to residual-type estimators, we introduce some estimators that are couched in the ideas and techniques of domain decomposition. Results of numerical experiments are presented.

Guaranteed and Fully Robust a posteriori Error Estimates for Conforming Discretizations of Diffusion Problems with Discontinuous Coefficients

We study in this paper a posteriori error estimates for H-conforming numerical approximations of diffusion problems with a diffusion coefficient piecewise constant on the mesh cells but arbitrarily discontinuous across the interfaces between the cells. Our estimates give a global upper bound on the error measured either as the energy norm of the difference between the exact and approximate solu...