Finite Element Discretizations for Incompressible Flow on Split Meshes

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Meeting ID: 933 610 9307
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Meeting ID: 933 610 9307
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Thursday, September 24, 2020 - 14:00


Speaker Information
Michael J. Neilan
University of Pittsburgh

Abstract or Additional Information

We construct families of divergence-free finite element methods for the Stokes/Navier-Stokes problem. Borrowing tools from the theory of multi-variate splines, we define these spaces on splits of a simplicial triangulation. We show that the divergence-free Stokes finite element pairs are connected to smooth piecewise polynomial spaces via a smooth discrete de Rham complex. Byproducts of this construction include characterizations of discrete divergence-free subspaces for the Stokes problem, commutative projections, and simple formulas for the dimensions of smooth polynomial spaces.