9 papers · 1 filter
Construction of trace-preserving Fortin operators
Franziska Eickmann, Tabea Tscherpel
We present a unifying framework to construct local Fortin operators for conforming mixed finite element pairs for the Stokes equations. The operators are constructed to satisfy the…
Sobolev stability of the -projection on hybrid meshes
Lars Diening, Viktoria Lingert, Tabea Tscherpel
We establish - and -stability of the -projection onto mapped Lagrange finite elements on hybrid meshes consisting of triangles and convex quadrilaterals arising…
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 posteriori existence of strong solutions to the Navier-Stokes equations in 3D
Aaron Brunk, Jan Giesselmann, Tabea Tscherpel
Global existence of strong solutions to the three-dimensional incompressible Navier-Stokes equations remains an open problem. A posteriori existence results offer a way to rigorous…
Scott-Vogelius element and iterated penalty method for inhomogeneous Dirichlet boundary conditions
Franziska Eickmann, L. Ridgway Scott, Tabea Tscherpel
We present quasi-optimal a priori error estimates for general mixed finite element methods to approximate solutions of the Stokes problem subject to inhomogeneous Dirichlet boundar…
A Nitsche method for incompressible fluids with general dynamic boundary conditions
Pablo Alexei Gazca-Orozco, Franz Gmeineder, Erika Maringová Kokavcová +1
Both Newtonian and non-Newtonian fluids may exhibit complex slip behaviour at the boundary. We examine a broad class of slip boundary conditions that generalises the commonly used…