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Texas A&M University

Numerical Analysis Seminar

Date: November 29, 2023

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Michael Neilan, University of Pittsburg


Title: Divergence-free finite element spaces for incompressible flow on isoparametric meshes

Abstract: In this talk, we construct and analyze an isoparametric and divergence-free finite element pair for the Stokes problem. The pair is defined by mapping the Scott-Vogelius finite element space via a non-traditional Piola transform. The velocity space has the same degrees of freedom as the canonical Lagrange finite element space, and the proposed spaces reduce to the Scott-Vogelius pair in the interior of the domain. The resulting method converges with optimal order, is divergence--free, and is pressure robust. In the second part of the talk, we extend this isoparametric framework to construct a stable and strongly conforming pair. This is achieved by constructing a new divergence-preserving (Piola) mapping combined with an enriching strategy that imposes full continuity across shared edges in the isoparametric mesh.