20 citations · 47 across the 20 of their papers we have counts for
23 papers
An explicit factorization of the Green's function for an acoustic half-space problem with impedance boundary conditions into an oscillatory exponential and a slowly varying function
C. Lin, J. M. Melenk, S. Sauter
In this paper, new representations of the Green's function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of t…
Skeleton Integral Equations for Acoustic Transmission Problems with Varying Coefficients
Francesco Florian, Ralf Hiptmair, Stefan A. Sauter
In this paper we will derive an non-local (``integral'') equation which transforms a three-dimensional acoustic transmission problem with \emph{variable} coefficients, non-zero abs…
The pressure-wired Stokes element: a mesh-robust version of the Scott-Vogelius element
Benedikt Gräßle, Nis-Erik Bohne, Stefan A. Sauter
The Scott-Vogelius finite element pair for the numerical discretization of the stationary Stokes equation in 2D is a popular element which is based on a continuous velocity approxi…
On the Inf-Sup Stability of Crouzeix-Raviart Stokes Elements in 3D
Stefan Sauter, Céline Torres
We consider non-conforming discretizations of the stationary Stokes equation in three spatial dimensions by Crouzeix-Raviart type elements. The original definition in the seminal p…
Wavenumber-explicit hp-FEM analysis for Maxwell's equations with impedance boundary conditions
Jens M. Melenk, Stefan A. Sauter
The time-harmonic Maxwell equations at high wavenumber k in domains with an analytic boundary and impedance boundary conditions are considered. A wavenumber-explicit stability and…
Critical Functions and Inf-Sup Stability of Crouzeix-Raviart Elements
C. Carstensen, S. Sauter
In this paper, we prove that Crouzeix-Raviart finite elements of polynomial order , odd, are inf-sup stable for the Stokes problem on triangulations. For , …
Solvability of Discrete Helmholtz Equations
Maximilian Bernkopf, Stefan Sauter, Céline Torres +1
We study the unique solvability of the discretized Helmholtz problem with Robin boundary conditions using a conforming Galerkin -finite element method. Well-posedness of the di…
The Heterogeneous Helmholtz Problem with Spherical Symmetry: Green's Operator and Stability Estimates
Stefan Sauter, Céline Torres
We study wave propagation phenomena modelled in the frequency domain by the Helmholtz equation in heterogeneous media with focus on media with discontinuous, highly oscillating wav…
Stabilized leapfrog based local time-stepping method for the wave equation
Marcus J. Grote, Simon Michel, Stefan Sauter
Local time-stepping methods permit to overcome the severe stability constraint on explicit methods caused by local mesh refinement without sacrificing explicitness. In \cite{DiazGr…
A Stable Boundary Integral Formulation of an Acoustic Wave Transmission Problem with Mixed Boundary Conditions
Sarah Eberle, Francesco Florian, Ralf Hiptmair +1
In this paper, we consider an acoustic wave transmission problem with mixed boundary conditions of Dirichlet, Neumann, and impedance type. The transmission interfaces may join the…
Wave number-Explicit Analysis for Galerkin Discretizations of Lossy Helmholtz Problems
Jens M. Melenk, Stefan A. Sauter, Céline Torres
We present a stability and convergence theory for the lossy Helmholtz equation and its Galerkin discretization. The boundary conditions are of Robin type. All estimates are explici…
Variable Order, Directional H2-Matrices for Helmholtz Problems with Complex Frequency
Steffen Börm, Maria Lopez-Fernandez, Stefan Sauter
The sparse approximation of high-frequency Helmholtz-type integral operators has many important physical applications such as problems in wave propagation and wave scattering. The…
Benchmark computation of eigenvalues with large defect for non-selfadjoint elliptic differential operators
Rebekka Gasser, Joscha Gedicke, Stefan Sauter
In this paper we present benchmark problems for non-selfadjoint elliptic eigenvalue problems with large defect and ascent. We describe the derivation of the benchmark problem with…
Numerical approximation of Poisson problems in long domains
Michel Chipot, Wolfgang Hackbusch, Stefan Sauter +1
In this paper, we consider the Poisson equation on a "long" domain which is the Cartesian product of a one-dimensional long interval with a (d-1)-dimensional domain. The right-hand…
Wavenumber-explicit -FEM analysis for Maxwell's equations with transparent boundary conditions
Jens Markus Melenk, Stefan Sauter
The time-harmonic Maxwell equations at high wavenumber are discretized by edge elements of degree on a mesh of width . For the case of a ball and exact, transparent boun…
Stability estimate for the Helmholtz equation with rapidly jumping coefficients
Stefan Sauter, Celine Torres
The goal of this paper is to investigate the stability of the Helmholtz equation in the high- frequency regime with non-smooth and rapidly oscillating coefficients on bounded domai…
A Posteriori Modelling-Discretization Error Estimate for Elliptic Problems with L ^\infty -Coefficients
M. Weymuth, S. Sauter, S. Repin
We consider elliptic problems with complicated, discontinuous diffusion tensor . One of the standard approaches to numerically treat such problems is to…
Convergence analysis of energy conserving explicit local time-stepping methods for the wave equation
Marcus J. Grote, Michaela Mehlin, Stefan Sauter
Local adaptivity and mesh refinement are key to the efficient simulation of wave phenomena in heterogeneous media or complex geometry. Locally refined meshes, however, dictate a sm…
A Family of Crouzeix-Raviart Finite Elements in 3D
Patrick Ciarlet, Charles F. Dunkl, Stefan A. Sauter
In this paper we will develop a family of non-conforming "Crouzeix-Raviart" type finite elements in three dimensions. They consist of local polynomials of maximal degree $p\in\math…
A Fully Discrete Galerkin Method for Abel-type Integral Equations
Urs Vögeli, Khadijeh Nedaiasl, Stefan A. Sauter
In this paper, we present a Galerkin method for Abel-type integral equation with a general class of kernel. Stability and quasi-optimal convergence estimates are derived in raction…
A Posteriori Error Estimation of hp-dG Finite Element Methods for Highly Indefinite Helmholtz Problems (extended version)
Stefan Sauter, Jakob Zech
In this paper, we will consider an -finite elements discretization of a highly indefinite Helmholtz problem by some dG formulation which is based on the ultra-weak variational…
Functional Estimates for Derivatives of the Modified Bessel Function and related Exponential Functions
Silvia Falletta, Stefan A. Sauter
Let denote the modified Bessel function of second kind and zeroth order. In this paper we will studying the function $\tildeω_{n}\left( x\right) :=\frac{\left( -x\right) ^{…
The intersection of bivariate orthogonal polynomials on triangle patches
Tom H. Koornwinder, Stefan A. Sauter
In this paper, the intersection of bivariate orthogonal polynomials on triangle patches will be investigated. The result is interesting by its own but also has important applicatio…