A methodology for adaptive finite element analysis: Towards an integrated computational environment

This work introduces a methodology for self-adaptive numerical procedures, which relies on the various components of an integrated, object-oriented, c omputational environment involving pre-, analysis, and post-processing modu les. A basic platform for numerical experiments and further development is provided, which allows implementation of new elements/error estimators and sensitivity analysis. A general implementation of the Superconvergent Patch Recovery (SPR) and the recently proposed Recovery by Equilibrium in Patche s (REP) is presented. Both SPR and REP are compared and used for error esti mation and for guiding the adaptive remeshing process. Moreover, the SPR is extended for calculating sensitivity quantities of first and higher orders . The mesh (re-)generation process is accomplished by means of modern metho ds combining quadtree and Delaunay triangulation techniques. Surface mesh g eneration in arbitrary domains is performed automatically (i.e. with no use r intervention) during the self-adaptive analysis using either quadrilatera l or triangular elements. These ideas are implemented in the Finite Element System Technology in Adaptivity (FESTA) software. The effectiveness and ve rsatility of FESTA are demonstrated by representative numerical examples il lustrating the interconnections among finite element analysis, recovery pro cedures, error estimation/adaptivity and automatic mesh generation.