54 citations · 299 across the 38 of their papers we have counts for
9 papers · 1 filter
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…
Theory of shifts, shocks, and the intimate connections to -type a posteriori error analysis of numerical schemes for hyperbolic problems
Jan Giesselmann, Sam G. Krupa
In this paper, we develop reliable a posteriori error estimates for numerical approximations of scalar hyperbolic conservation laws in one space dimension. Our methods have no inhe…
Regularity and long time behavior of a doubly nonlinear parabolic problem and its discretization
Herbert Egger, Jan Giesselmann
We study a doubly nonlinear parabolic problem arising in the modeling of gas transport in pipelines. Using convexity arguments and relative entropy estimates we show uniform bounds…
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…
An Observer for pipeline flow with hydrogen blending in gas networks: exponential synchronization
Martin Gugat, Jan Giesselmann
We consider a state estimation problem for gas flows in pipeline networks where hydrogen is blended into the natural gas. The flow is modeled by the quasi-linear isothermal Euler e…
Observer-based data assimilation for barotropic gas transport using distributed measurements
Jan Giesselmann, Martin Gugat, Teresa Kunkel
We consider a state estimation problem for gas pipeline flow modeled by the one-dimensional barotropic Euler equations. In order to reconstruct the system state, we construct an ob…
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…