AN ADAPTIVE STRATEGY FOR ELLIPTIC PROBLEMS INCLUDING A-POSTERIORI CONTROLLED BOUNDARY APPROXIMATION

We derive a posteriori error estimates for the approximation of linear elliptic problems on domains with piecewise smooth boundary. The nume rical solution is assumed to be defined on a Finite Element mesh, whos e boundary vertices are located on the boundary of the continuous prob lem. No assumption is made on a geometrically fitting shape. A posteri ori error estimates are given in the energy norm and the L-2-norm, and efficiency of the adaptive algorithm is proved in the case of a satur ated boundary approximation. Furthermore, a strategy is presented to c ompute the effect of the non-discretized part of the domain on the err or starting from a coarse mesh. This especially implies that parts of the domain, where the measured error is small, stay non-discretized. T he presented algorithm includes a stable path following to supply a su fficient polygonal approximation of the boundary, the reliable computa tion of the a posteriori estimates and a mesh adaptation based on Dela unay techniques. Numerical examples illustrate that errors outside the initial discretization will be detected.