54 citations · 299 across the 38 of their papers we have counts for
27 papers · 1 filter
A posteriori analysis for nonlinear convection-diffusion systems
Andreas Dedner, Jan Giesselmann, Kiwoong Kwon +1
This work provides reliable a posteriori error estimates for Runge-Kutta discontinuous Galerkin approximations of nonlinear convection-diffusion systems. The classes of systems we…
A posteriori error control for a finite volume scheme for a cross-diffusion model of ion transport
Arne Berrens, Jan Giesselmann
We derive a reliable a posteriori error estimate for a cell-centered finite volume scheme approximating a cross-diffusion system modeling ion transport through nanopores. To this e…
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-…
A priori error estimates of Runge-Kutta discontinuous Galerkin schemes to smooth solutions of fractional conservation laws
Fabio Leotta, Jan Giesselmann
We give a priori error estimates of second order in time fully explicit Runge-Kutta discontinuous Galerkin schemes using upwind fluxes to smooth solutions of scalar fractional cons…
A posteriori error analysis of a positivity preserving scheme for the power-law diffusion Keller-Segel model
Jan Giesselmann, Niklas Kolbe
We study a finite volume scheme approximating a parabolic-elliptic Keller-Segel system with power law diffusion with exponent and periodic boundary conditions. We deri…
A posteriori error control for a Discontinuous Galerkin approximation of a Keller-Segel model
Jan Giesselmann, Kiwoong Kwon
We provide a posteriori error estimates for a discontinuous Galerkin scheme for the parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are conditional…
Stability of step size control based on a posteriori error estimates
Hendrik Ranocha, Jan Giesselmann
A posteriori error estimates based on residuals can be used for reliable error control of numerical methods. Here, we consider them in the context of ordinary differential equation…
A-posteriori error estimates for systems of hyperbolic conservation laws
Jan Giesselmann, Aleksey Sikstel
We provide rigorous and computable a-posteriori error estimates for first order finite-volume approximations of nonlinear systems of hyperbolic conservation laws in one spatial dim…
Model adaptation for hyperbolic balance laws
Jan Giesselmann, Hrishikesh Joshi, Siegfried Müller +1
In this work, we devise a model adaptation strategy for a class of model hierarchies consisting of two levels of model complexity. In particular, the fine model consists of a syste…
Improving Weak PINNs for Hyperbolic Conservation Laws: Dual Norm Computation, Boundary Conditions and Systems
Aidan Chaumet, Jan Giesselmann
We consider the approximation of entropy solutions of nonlinear hyperbolic conservation laws using neural networks. We provide explicit computations that highlight why classical PI…
On the convergence of the regularized entropy-based moment method for kinetic equations
Graham W. Alldredge, Martin Frank, Jan Giesselmann
The entropy-based moment method is a well-known discretization for the velocity variable in kinetic equations which has many desirable theoretical properties but is difficult to im…
A posteriori error estimates for wave maps into spheres
Jan Giesselmann, Elena Mäder-Baumdicker, David Jakob Stonner
We provide a posteriori error estimates in the energy norm for temporal semi-discretisations of wave maps into spheres that are based on the angular momentum formulation. Our analy…
Data-Driven Snapshot Calibration via Monotonic Feature Matching
Neeraj Sarna, Jan Giesselmann, Peter Benner
Snapshot matrices of hyperbolic equations have a slow singular value decay, resulting in inefficient reduced-order models. We develop on the idea of inducing a faster singular valu…
Error control for statistical solutions
Jan Giesselmann, Fabian Meyer, Christian Rohde
Statistical solutions have recently been introduced as a an alternative solution framework for hyperbolic systems of conservation laws. In this work we derive a novel a posteriori…
An a posteriori error analysis based on non-intrusive spectral projections for systems of random conservation laws
Jan Giesselmann, Fabian Meyer, Christian Rohde
We present an a posteriori error analysis for one-dimensional random hyperbolic systems of conservation laws. For the discretization of the random space we consider the Non-Intrusi…
Residual estimates for post-processors in elliptic problems
Andreas Dedner, Jan Giesselmann, Tristan Pryer +1
In this work we examine a posteriori error control for post-processed approximations to elliptic boundary value problems. We introduce a class of post-processing operator that `twe…
A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws
Jan Giesselmann, Fabian Meyer, Christian Rohde
In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for i…
Convergence Analysis of the Grad's Hermite Approximation to the Boltzmann Equation
Neeraj Sarna, Jan Giesselmann, Manuel Torrilhon
In (Commun Pure Appl Math 2(4):331-407, 1949), Grad proposed a Hermite series expansion for approximating solutions to kinetic equations that have an unbounded velocity space. Howe…
A posteriori error analysis for random scalar conservation laws using the Stochastic Galerkin method
Jan Giesselmann, Fabian Meyer, Christian Rohde
In this article we present an a posteriori error estimator for the spatial-stochastic error of a Galerkin-type discretisation of an initial value problem for a random hyperbolic co…
A posteriori analysis for dynamic model adaptation in convection dominated problems
Jan Giesselmann, Tristan Pryer
In this work we present an a posteriori error indicator for approximation schemes of Runge-Kutta-discontinuous-Galerkin type arising in applications of compressible fluid flows. Th…
A posteriori analysis of discontinuous Galerkin schemes for systems of hyperbolic conservation laws
Jan Giesselmann, Charalambos Makridakis, Tristan Pryer
In this work we construct reliable a posteriori estimates for some discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appro…
Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics
Jan Giesselmann, Tristan Pryer
We give an a posteriori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density…
Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics
Jan Giesselmann, Tristan Pryer
We give an a priori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics which involves an energy density depen…
Low Mach Asymptotic Preserving Scheme for the Euler-Korteweg Model
Jan Giesselmann
We present an all speed scheme for the Euler-Korteweg model. We study a semi-implicit time-discretisation which treats the terms, which are stiff for low Mach numbers, implicitly a…