A Posteriori Error Analysis and Adaptive Algorithms for Variational Inequalities

University Of Iowa, Iowa City IA

Investigators

Abstract

The objective of this project is to develop a systematic theory on a posteriori error estimation and adaptive algorithms for finite element solutions of variational inequalities. A posteriori error estimates play an essential role in assessing the reliability of numerical solutions and in developing efficient adaptive algorithms. Although several standard techniques have been developed to derive and analyze a posteriori error estimates for finite element solutions of differential equation problems, they do not work directly for a posteriori error analysis of numerical solutions of variational inequalities. In the proposed research, the duality theory of nonlinear analysis will be employed as a basic mathematical tool for the development of a posteriori error estimates of numerical solutions of variational inequalities. Variational inequalities form an important family of nonlinear problems arising in a wide range of applications. A partial list of the applications where variational inequalities arise include contact mechanics, plasticity, non-Newtonian fluid flows, metal forming, metal extrusion, financial mathematics. A systematic approach will be developed to derive a posteriori error estimates and to form and test efficient, reliable adaptive solution algorithms for finite element approximations of variational inequalities. The research results will have a direct impact on many areas of science and technology.