An adaptive finite element method for a linear elliptic equation with variable coefficients

We study the adaptive finite element method to solve linear elliptic bounda ry value problems on bounded domains in R-2 For this we first prove a poste riori error estimates that carefully tate data error into account and show convergence an adaptive algorithm. Then we propose an adaptive method that may start from very coarse meshes. A numerical example underlines the neces sity of monitoring the data error in applications. Moreover, we can show th at the a posteriori error bound of our proposed error estimator will (in a simple model situation) not depend on jumps in the coefficient of the main part of the equation when the lines of discontinuity are resolved by the me sh.