Thursday, Aug 17, 2017 - 3:30pm - Allen 14
A unified analysis of quasi-optimal convergence for adaptive mixed finite element methods
Dr. Guozhu Yu, Mathematics, Southwest Jiaotong University, China
Title: A unified analysis of quasi-optimal convergence for adaptive mixed finite element methods
Abstract: In this talk, we present a unified analysis of both convergence and optimality of adaptive mixed finite element methods for a class of problems when the finite element spaces and corresponding a posteriori error estimates under consideration satisfy five hypotheses. The main ingredient for the analysis is a new method to analyze both discrete reliability and quasi-orthogonality. This new method arises from an appropriate and natural choice of the norms for both the discrete displacement and stress spaces, and a newly defined projection operator from the discrete stress space on the coarser mesh onto the discrete divergence free space on the finer mesh. As applications, we prove these five hypotheses for the Raviart--Thomas and Brezzi--Douglas--Marini elements of the Poisson and Stokes problems in both 2D and 3D.