9 papers
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…
On Korn inequalities with lower order trace terms
Franz Gmeineder, Endre Süli, Tabea Tscherpel
We give an elementary estimate that entails and generalises numerous Korn inequalities scattered in the literature. As special instances, we obtain general Korn-type inequalities i…
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…