Recovery Type A Posteriori Error Estimates

Wayne State University, Detroit MI

Investigators

Abstract

Zhang The investigator studies a posteriori error estimates for the numerical solution of partial differential equations. He develops general mathematical theory for recovery type a posteriori error estimates and explores a new gradient recovery technique and associated error estimator that has better properties than the existing ones. Some recent mathematical theory in finite element superconvergence, asymptotic regularity, as well as improved interior analysis, is employed in the project. Numerical solutions of differential equations are essential in all areas of science and engineering. But the numerical solutions are often less accurate than one desires. It is therefore important to estimate the error and to use that estimate to improve the accuracy. Error estimation is essential for effective and reliable computation. Recovery type a posteriori error estimates are post-processing techniques that use a numerical solution produced by some base method to produce approximations that are of higher order of accuracy than the base method solution, and that combine the two solutions to estimate the error in the approximate solution. The techniques are common but not theoretically understood or justified, especially for nonuniform meshes. The investigator studies these methods and develops a new kind of recovery type error estimator that offers some advantages over present alternatives. The project fills a gap between engineering practice and mathematical theoretical development. The project includes training of graduate students. There are interdisciplinary connections with engineers and other scientific computing disciplines, and with industry.