27 citations · 68 across the 15 of their papers we have counts for
15 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…
Exact Integration for singular Zienkiewicz and Guzman-Neilan Finite Elements with Implementation
Lars Diening, Johannes Storn, Tabea Tscherpel
We develop a recursive integration formula for a class of rational polynomials in 2D. Based on this, we present implementations of finite elements that have rational basis function…
Energy-consistent Petrov-Galerkin time discretization of port-Hamiltonian systems
Jan Giesselmann, Attila Karsai, Tabea Tscherpel
For a general class of nonlinear port-Hamiltonian systems we develop a high-order time discretization scheme with certain structure preservation properties. The finite or infinite-…
Grading of Triangulations Generated by Bisection
Lars Diening, Johannes Storn, Tabea Tscherpel
For triangulations generated by the adaptive bisection algorithm by Maubach and Traxler we prove existence of a regularized mesh function with grading two. This sharpens previous r…
Dimensions of exactly divergence-free finite element spaces in 3D
L. Ridgway Scott, Tabea Tscherpel
We examine the dimensions of various inf-sup stable mixed finite element spaces on tetrahedral meshes in 3D with exact divergence constraints. More precisely, we compare the standa…
Interpolation Operator on negative Sobolev Spaces
Lars Diening, Johannes Storn, Tabea Tscherpel
We introduce a Scott--Zhang type projection operator mapping to Lagrange elements for arbitrary polynomial order. In addition to the usual properties, this operator is compatible w…
A class of boundary conditions for time-discrete Green-Naghdi equations with bathymetry
Sebastian Noelle, Martin Parisot, Tabea Tscherpel
This work is devoted to the structure of the time-discrete Green-Naghdi equations including bathymetry. We use the projection structure of the equations to characterize homogeneous…
Fortin Operator for the Taylor-Hood Element
Lars Diening, Johannes Storn, Tabea Tscherpel
We design a Fortin operator for the lowest-order Taylor-Hood element in any dimension, which was previously constructed only in 2D. In the construction we use tangential edge bubbl…
On the Sobolev and -Stability of the -projection
Lars Diening, Johannes Storn, Tabea Tscherpel
We show stability of the -projection onto Lagrange finite element spaces with respect to (weighted) and -norms for any polynomial degree and for any space dimen…
Fully discrete finite element approximation of unsteady flows of implicitly constituted incompressible fluids
Endre Süli, Tabea Tscherpel
Implicit constitutive theory provides a very general framework for fluid flow models, including both Newtonian and generalized Newtonian fluids, where the Cauchy stress tensor and…