An Adaptive Finite Element Method for a Linear Elliptic Equation with Variable Coefficients

Abstract

We study the adaptive finite element method to solve linear elliptic boundary value problems on bounded domains in ℝ2. For this we first prove a posteriori error estimates that carefully take data error into account and show convergence of an adaptive algorithm. Then we propose an adaptive method that may start from very coarse meshes. A numerical example underlines the necessity of monitoring the data error in applications. Moreover, we can show that 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 mesh.