Physical Sciences and Mathematics Commons^™

Recovery Techniques For Finite Element Methods And Their Applications, Hailong Guo

Wayne State University Dissertations

Recovery techniques are important post-processing methods to obtain improved approximate solutions from primary data with reasonable cost. The practical us- age of recovery techniques is not only to improve the quality of approximation, but also to provide an asymptotically exact posteriori error estimators for adaptive meth- ods. This dissertation presents recovery techniques for nonconforming finite element methods and high order derivative as well as applications of gradient recovery.

Our first target is to develop a systematic gradient recovery technique for Crouzeix- Raviart element. The proposed method uses finite element solution to build a better approximation of the exact gradient based …