Producing Divergence-free Approximations with the Scott-Vogelius Finite Elements

Friday, June 30, 2017 - 10:10am - 11:00am
Keller 3-180
Johnny Guzman (Brown University)
In recent years there has been an interest in finding finite element spaces that yield divergence free approximation for incompressible flows. One of the original finite elements spaces were provided by Scott and Vogelius. The velocity space consist of continuous vector fields that are piecewise polynomials of degree k and the pressure space consist of piecewise polynomials of degree k-1 (with certain restrictions if singular vertices are present). In 1985, Scott and Vogelius proved that for k greater than or equal to 4 these spaces are inf-sup stable. In this talk we start by discussing, an alternative proof that relaxes the conditions imposed in the original 1985 paper. More importantly, we discuss how the new proof guides us to prove inf-sup stability in the k=3 case on a large class of meshes. This is joint work with Ridgway Scott.