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The Delaunay incremental insertion method for tetrahedral grid generation can be used for the automatic generation of unstructured grids made up of tetrahedra and prisms. This method has been shown to be robust for complex geometries, with no user intervention required during the grid generation process. It has been demonstrated that the Delaunay background grid can be efficiently used as the data structure for checking prism intersections and for the automatic termination of prism generation.

An algorithm used for adaptive refinement of three-dimensional finite element tetrahedral meshes is simple and does not produce any nonconforming elements during refinement. The use of this algorithm for mesh refinement does not significantly change the aspect ratio of the element. This procedure provides an efficient solution of three-dimensional models for linear strain or higher order elements.