An optimal adaptive mixed finite element method

Abstract. Various applications in uid dynamics and computational continuum mechanics motivate the development of reliable and ecient adaptive algorithms for mixed nite element methods. In order to save degrees of freedom, not all but just some selected set of nite element domains are rened. Hence the fundamental question of convergence as well as the question of optimality require new mathematical arguments. The presented adaptive algorithm for Raviart-Thomas mixed nite element methods solves the Poisson model problem, with optimal convergence rate. Chen, Holst, and Xu presented convergence and optimality of adaptive mixed nite element methods (2008) following arguments of Rob Stevenson for the conforming nite element method. Their algorithm reduces oscillations separately, before approximating the solution by some adaptive algorithm in the spirit of W. Dörer (1996). The algorithm proposed here appears more natural in switching to either reduction of the edge-error estimator ...

• Type: Journal
• Year: 2011
• Where: MOC
• Authors: Carsten Carstensen, Hella Rabus
• Keywords: Adaptive Algorithm, Intelligent Agents, Mixed Nite Element, MOC 2011, Nite Element Method