8 papers
A local Fortin projection for the Scott-Vogelius elements on general meshes
Franziska Eickmann, Johnny Guzmán, Michael Neilan +2
We construct a local Fortin projection for the Scott-Vogelius finite element pair for polynomial degree on general shape-regular triangulations in two dimensions. In part…
A Divergence-Free Scott-Vogelius Finite Element Method for the Surface Stokes Problem
Yerim Kone, Michael Neilan, David Poling
We construct and analyze an exactly divergence-free Scott-Vogelius finite element method for the surface Stokes problem. The proposed scheme simultaneously enforces the tangentiali…
On the convergence of iterated penalty methods for structure-preserving discretizations of saddle point problems
Patrick E. Farrell, Michael Neilan, Charles Parker +1
We present new convergence estimates for the iterated penalty method applied to structure-preserving discretizations of linear generalized saddle point systems. The method may be v…
A TraceFEM Interior Penalty Method for the Surface Biharmonic Equation
Michael Neilan, Hongzhi Wan
We construct and analyze a TraceFEM discretization for the surface biharmonic problem. The method utilizes standard quadratic Lagrange finite element spaces defined on a three-dime…
An unfitted divergence-free higher order finite element method for the Stokes problem
Michael Neilan, Maxim Olshanskii, Henry von Wahl
The paper develops and analyzes a higher-order unfitted finite element method for the incompressible Stokes equations, which yields a strongly divergence-free velocity field up to…
A Taylor-Hood finite element method for the surface Stokes problem without penalization
Alan Demlow, Michael Neilan
Finite element approximation of the velocity-pressure formulation of the surfaces Stokes equations is challenging because it is typically not possible to enforce both tangentiality…