Title: Bernstein polynomials: Universal simplicial finite element shape functions?

Speaker: Robert Kirby, Texas Tech University

Date/Time: Monday, April 12, 2010, 9:00-10:00 am        

Location: CSRI Building/Room 90 (Sandia NM)

Brief Abstract: The Bernstein polynomials are known classically in approximation theory and widely used in various aspects of computational geometry, but are only recently being considered in the context of finite element shape functions.  In this talk, I will show that Bernstein polynomials on the simplex possess a special structure that allows a wide class of finite element operators to be evaluated with "spectral element complexity", including operators with variable coefficients.

Moreover, spline spaces over triangulations and exterior calculus bases for H(div) and H(curl) may also be expressed locally in terms of Bernstein polynomials, so that the techniques I describe will eventually be applicable beyond standard C^0 finite element spaces.

CSRI POC: Pavel Bochev, 505-844-1990