Error estimates for the finite-element solution of an elliptic singularly perturbed problem

e-mail:ang{at}am.uni-erlangen.de The paper deals with an upwind discretization of finite-volume-typefor singularly perturbed elliptic boundary value problems. Stability,inverse monotonicity and convergence are considered. The mainobjective is to pursue the dependence of the error estimateon the perturbation parameter.     

An a posteriori estimation for the solution of elliptic boundary value problems by means of upwind FEM

The paper presents a theory for a posteriori error estimationof finite element solutions of two-dimensional convection-diffusionequations which are discretized by means of an upwind method.The main theorem gives an error estimation in terms of approximatelycomputable and localized quantities.