On automatic mesh construction and mesh refinement in finite element analysis

A valuable approach for the automatic generation of effective finite element meshes is presented. The approach comprises, firstly, an initial mesh construction and, secondly, an h-version of adaptive refinement based on an error analysis. For the initial mesh construction, a robust triangulation scheme for 2D analysis and tetrahedronization scheme for 3D analysis are used, in which the elements are generated from the outside boundaries. For the adaptive refinement process, an error indicator is used with a relaxation factor to obtain efficient solutions. The initial mesh construction schemes have been implemented for 2D and 3D analyses whereas the self-adaptive mesh improvement procedure has only been implemented for 2D analysis. Example solutions are given to demonstrate the solution procedures.