Optimal discretization based refinement criteria for finite element adaption

Abstract

One of the major research issues in adaptive finite element analysis is the feedback control system used to guide the adaption. Essentially, one needs to resolve which error data to feedback after each iteration, and how to use it to initialize the next adaptive step. Variational aspects of optimal discretizations for scalar Poisson and Helmholtz systems are used to derive new refinement criteria for adaptive finite element solvers. They are shown to be effective and economical for h-, p- and hp-schemes.