Title: Pyramidal finite elements

Speaker: Joel Phillips, Department of Mathematics, University College, London, United Kingdom

Date/Time: Tuesday, February 15, 2011, 9:00 am MST       

Location: CSRI Building/Room 90 (Sandia NM)

Brief Abstract: Pyramidal finite elements are useful as glue between tetrahedra and hexahedra in hybrid meshes. I will give a brief history of attempts to build pyramidal elements and explain why it's a challenging problem. In particular, we will see that it is impossible to build a pyramidal finite element using purely polynomial basis functions, which in turn means that the standard arguments for the effect of numerical integration on finite elements require a little delicate revision. I will describe our construction of arbitrarily high order elements for each of the spaces of the de Rham complex (i.e. H^1, H(curl), H(div) and L^2). These elements satisfy a commuting diagram property and are compatible with the relevant hexahedral and tetrahedral elements. I will also give some details of a reference implementation of the elements and show some simple numerical experiments.

CSRI POC: Pavel Bochev, 505-844-1990