Northern Illinois University
New and Old Rectangular Mixed Finite Elements
Abstract: In recent years, the concept of structure preserving discretization has taken a prominent role in the design and analysis of numerical methods for partial differential equations. Using differential complexes and the structure revealed by the finite element exterior calculus, we found canonical H(div) and H(curl) finite elements on rectangular meshes. The new elements with the serendipity elements form a discrete version of the de Rham complex. For the latter, we give a dimension independent definition. Differential complexes are combined through the Arnold-Falk-Winther construction to obtain new rectangular elements for elasticity with weakly imposed symmetry condition. The new rectangular elements are compared with some older elements.
Wednesday January 11, 2012 at 3:00 PM in SEO 636