28 citations · 48 across the 16 of their papers we have counts for
16 papers · 1 filter
A Stable Boundary Element Method for Reliable Long-Time Industrial Sound Emission
Simon Schneider, Ceyhun Özdemir, Heiko Gimperlein +2
In this paper we investigate a stable space-time formulation for long-time industrial sound emission problems. To this end, we use a well-posed Galerkin formulation in space and ti…
The Kolmogorov N-width for linear transport: Exact representation and the influence of the data
Florian Arbes, Constantin Greif, Karsten Urban
The Kolmogorov -width describes the best possible error one can achieve by elements of an -dimensional linear space. Its decay has extensively been studied in Approximation T…
An Ultra-Weak Space-Time Variational Formulation for the Schrödinger Equation
Stefan Hain, Karsten Urban
We present a well-posed ultra-weak space-time variational formulation for the time-dependent version of the linear Schrödinger equation with an instationary Hamiltonian. We prove o…
An ultraweak variational method for parameterized linear differential-algebraic equations
Emil Beurer, Moritz Feuerle, Niklas Reich +1
We investigate an ultraweak variational formulation for (parameterized) linear differential-algebraic equations (DAEs) w.r.t. the time variable which yields an optimally stable sys…
Very Weak Space-Time Variational Formulation for the Wave Equation: Analysis and Efficient Numerical Solution
Julian Henning, Davide Palitta, Valeria Simoncini +1
We introduce a very weak space-time variational formulation for the wave equation, prove its well-posedness (even in the case of minimal regularity) and optimal inf-sup stability.…
Linear/Ridge expansions: Enhancing linear approximations by ridge functions
Constantin Greif, Philipp Junk, Karsten Urban
We consider approximations formed by the sum of a linear combination of given functions enhanced by ridge functions -- a Linear/Ridge expansion. For an explicitly or implicitly giv…
A Space-Time Variational Method for Optimal Control Problems: Well-posedness, stability and numerical solution
Nina Beranek, M. Alexander Reinhold, Karsten Urban
We consider an optimal control problem constrained by a parabolic partial differential equation (PDE) with Robin boundary conditions. We use a well-posed space-time variational for…
Matrix oriented reduction of space-time Petrov-Galerkin variational problems
Julian Henning, Davide Palitta, Valeria Simoncini +1
Variational formulations of time-dependent PDEs in space and time yield -dimensional problems to be solved numerically. This increases the number of unknowns as well as the…
Decay of the Kolmogorov -width for wave problems
Constantin Greif, Karsten Urban
The Kolmogorov -width describes the rate of the worst-case error (w.r.t.\ a subset of a normed space ) arising from a projection ont…
HT-AWGM: A Hierarchical Tucker-Adaptive Wavelet Galerkin Method for High Dimensional Elliptic Problems
Mazen Ali, Karsten Urban
This paper is concerned with the construction, analysis and realization of a numerical method to approximate the solution of high dimensional elliptic partial differential equation…
(Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov-Galerkin Methods
Julia Brunken, Kathrin Smetana, Karsten Urban
We consider ultraweak variational formulations for (parametrized) linear first order transport equations in time and/or space. Computationally feasible pairs of optimally stable tr…
A Hierarchical A-Posteriori Error Estimatorfor the Reduced Basis Method
Stefan Hain, Mario Ohlberger, Mladjan Radic +1
In this contribution we are concerned with tight a posteriori error estimation for projection based model order reduction of - stable parameterized variational problems…
A Reduced Basis Method for the Hamilton-Jacobi-Bellman Equation with Application to the European Union Emission Trading Scheme
Sebastian Steck, Karsten Urban
This paper draws on two sources of motivation: (1) The European Union Emission Trading Scheme (EU-ETS) aims at limiting the overall emissions of greenhouse gases. The optimal abate…
A Reduced Basis Method for Parabolic Partial Differential Equations with Parameter Functions and Application to Option Pricing
Antonia Mayerhofer, Karsten Urban
We consider the Heston model as an example of a parameterized parabolic partial differential equation. A space-time variational formulation is derived that allows for parameters in…
Reduced Basis Methods Based Upon Adaptive Snapshot Computations
Mazen Ali, Kristina Steih, Karsten Urban
We use asymptotically optimal \emph{adaptive} numerical methods (here specifically a wavelet scheme) for snapshot computations within the offline phase of the Reduced Basis Method…
An efficient space-time adaptive wavelet Galerkin method for time-periodic parabolic partial differential equations
Sebastian Kestler, Kristina Steih, Karsten Urban
We introduce a multitree-based adaptive wavelet Galerkin algorithm {for} space-time discretized linear parabolic partial differential equations, focusing on time-periodic problems.…