7 papers
Discrete reliability for high-order Crouzeix--Raviart finite elements
Nis-Erik Bohne, Stefan A. Sauter
In this paper, the adaptive numerical solution of a 2D Poisson model problem by Crouzeix-Raviart elements ( ) of arbitrary odd degree $…
Stable skeleton integral equations for general coefficient Helmholtz transmission problems
Benedikt Gräßle, Ralf Hiptmair, Stefan Sauter
A novel variational formulation of layer potentials and boundary integral operators generalizes their classical construction by Green's functions, which are not explicitly availabl…
Dirichlet-to-Neumann operator for the Helmholtz problem with general wavenumbers on the -sphere
Benedikt Gräßle, Stefan A. Sauter
This paper considers the Helmholtz problem in the exterior of a ball with Dirichlet boundary conditions and radiation conditions imposed at infinity. The differential Helmholtz ope…
Crouzeix-Raviart elements on simplicial meshes in dimensions
Nis-Erik Bohne, Patrick Ciarlet, Stefan Sauter
In this paper we introduce Crouzeix-Raviart elements of general polynomial order and spatial dimension for simplicial finite element meshes. We give explicit represent…
Pressure-improved Scott-Vogelius type elements
Nis-Erik Bohne, Benedikt Gräßle, Stefan A. Sauter
The Scott-Vogelius element is a popular finite element for the discretization of the Stokes equations which enjoys inf-sup stability and gives divergence-free velocity approximatio…
The inf-sup constant for -Crouzeix-Raviart triangular elements
S. Sauter
In this paper, we consider the discretization of the two-dimensional stationary Stokes equation by Crouzeix-Raviart elements for the velocity of polynomial order on confor…
Crouzeix-Raviart triangular elements are inf-sup stable
C. Carstensen, S. Sauter
The Crouzeix-Raviart triangular finite elements are - stable for the Stokes equations for any mesh with at least one interior vertex. This result affirms a {\em conject…