Basic Principles of Feedback and Adaptive Approaches in the Finite Element Method

摘要

The notion of feedback and adaptivity in numerical computations has attracted great attention in the recent years. All the modern ODE's solvers for initial value problems and quadratures are feedback methods. The feedback methods are increasingly in the focus of interest in the area of numerical solution of PDE and computational mechanics. Many reports, preprints and papers dealing with the adaptivity appeared recently. It seems to be that successful computation of today's large complex problems cannot be made without some kind of feedback or adaptive approach. This paper addresses the basic notions of the theory of feedback and adaptive finite element methods. An illustrative example of the finite element method for solving nonlinear differential equation of the elliptic type is presented. Numerical example of regridding process is given.