ADAPTIVE REFINEMENT CRITERION FOR ELLIPTIC PROBLEMS DISCRETIZED BY FEM

In a recent paper1 we presented a data structure to be used with multi grid techniques on non-homogeneously refined FEM meshes. This paper fo cuses on the adaptive refinement techniques used there. The error esti mate is obtained from standard Taylor series. For each element we comp ute its efficiency in terms of the size, the norm of the second deriva tives of the unknown and the parameter p, where L(p) is the chosen nor m. The way the norm influences the optimal mesh is studied. The number of elements to be refined at each step is such to produce a fast conv ergence to the optimal mesh, followed by successive homogeneous refine ments. We hope that the analysis of these two subjects could be of val ue for people working with other (perhaps very dissimilar) adaptive re finement techniques (error estimate and data structure, for instance).