Automatic and adaptive refinement of tetrahedral finite element meshes

An algorithm to adaptively remesh tetrahedral finite element meshes is presented. An indicator based on the estimator developed by Zienkiewicz and Zhu is used. This algorithm refines a given mesh only in areas of high stress concentration and thus avoids unnecessary subdivision of elements which are not near the stressed areas. In addition the element aspect ratio is not significantly degraded by the proposed algorithm. This is achieved by dividing only the longest edge of the element. Some example problems are presented to show the efficiency and robustness of the algorithm.