A Posteriori Error Estimates and Convergence of Error Indicator by FEM for a Semi-linear Elliptic Source-boundary Control Problem

In this paper, we obtain convergence of a posteriori error indicator to 0 when the mesh size h goes to 0 for the finite element approximation of source-boundary control problems governed by a system of semi-linear elliptic equations. We give the upper and lower bound of a posteriori error, and convergency of a posteriori error indicator.