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

• Published in: Computational mechanics 1999-06, Vol.23 (5-6), p.361-388
• Main Authors: PAULINO, G. H, MENEZES, I. F. M, CAVALCANTE NETO, J. B, MARTHA, L. F
• Format: Article
• Language: English
• Subjects: Applied sciences; Computation; Computational techniques; Computer aided design; Computer science; control theory; systems; Delaunay triangulation; Domains; Error analysis; Error detection; Exact sciences and technology; Finite element analysis; Finite element method; Finite-element and galerkin methods; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematical methods in physics; Mechanical engineering. Machine design; Mesh generation; Object-oriented programming; Physics; Post-processing; Quadrilaterals; Recovery; Self adaptive control systems; Sensitivity analysis; Software; Solid mechanics; Static elasticity; Static elasticity (thermoelasticity...); Structural and continuum mechanics
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s004660050416

This work introduces a methodology for self-adaptive numerical procedures, which relies on the various components of an integrated, object-oriented, computational environment involving pre-, analysis, and post-processing modules. 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 Patches (REP) is presented. Both SPR and REP are compared and used for error estimation 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 methods combining quadtree and Delaunay triangulation techniques. Surface mesh generation in arbitrary domains is performed automatically (i.e. with no user intervention) during the self-adaptive analysis using either quadrilateral or triangular elements. These ideas are implemented in the Finite Element System Technology in Adaptivity (FESTA) software. The effectiveness and versatility of FESTA are demonstrated by representative numerical examples illustrating the interconnections among finite element analysis, recovery procedures, error estimation/adaptivity and automatic mesh generation.