Three-dimensional automatic adaptive mesh generation

A technique for three-dimensional mesh refinement and adaptive mesh generation is presented. A procedure for refining three-dimensional tetrahedral meshes, based on Delaunay criteria, is developed. Additional nodes are inserted on an existing mesh and the tetrahedra produced are transformed, so that an optimum mesh is formed. Solution of a problem with an initial coarse mesh is followed by successive refinements. Furthermore, a posteriori error analysis is employed to estimate local errors and refine the mesh at those regions. A criterion of error estimation, the discontinuity of the normal field gradient on common interfaces, is proposed. Several examples using the proposed technique are presented to illustrate the usefulness of the method