A ROBUST ADAPTIVE STRATEGY FOR THE NONLINEAR POISSON EQUATION

Our goal is to develop adaptive strategies in order to obtain finite e lement solutions of the partial differential equation -Delta u=f(u) in a bounded domain Omega subset of R(2). In practice one works with an approximation f(h) of f. But this may give wrong results if we do not control the corresponding approximation error on coarse grids. In this work we develop a strategy that is robust, but less efficient, in the beginning of the adaptive algorithm and switches to a more efficient procedure if certain saturation conditions are satisfied. The results are based on a posteriori saturation criteria that measure the quality of the approximated solution.