A Convergent Adaptive Algorithm for Poisson’s Equation

We construct a converging adaptive algorithm for linear elements applied to Poisson’s equation in two space dimensions. Starting from a macro triangulation, we describe how to construct an initial triangulation from a priori information. Then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions. It is proved that the error, measured in the energy norm, decreases at a constant rate in each step until a prescribed error bound is reached. Extension to higher-order elements in two space dimension and numerical results are included.