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MultiWave: A computational laboratory for adaptive numerical methods approximating hyperbolic balance laws
Adrian Kolb, Aleksey Sikstel
The MultiWave C++-framework for adaptive numerical methods approximating hyperbolic balance laws is presented. MultiWave has been designed as a computational laboratory where new m…
Discontinuous Galerkin schemes for multi-dimensional coupled hyperbolic systems
Niklas Kolbe, Siegfried Müller, Aleksey Sikstel
A novel class of Runge-Kutta discontinuous Galerkin schemes for coupled systems of conservation laws in multiple space dimensions that are separated by a fixed sharp interface is i…
Coupled general Riemann problems for the Euler equations
Zhifang Du, Aleksey Sikstel
We introduce a novel method for systems of conservation laws coupled at a sharp interface based on generalized Riemann problems. This method yields a piecewise-linear in time appro…
An Entropy-Stable Discontinuous Galerkin Discretization of the Ideal Multi-Ion Magnetohydrodynamics System
Andrés M Rueda-Ramírez, Aleksey Sikstel, Gregor J Gassner
In this paper, we present an entropy-stable (ES) discretization using a nodal discontinuous Galerkin (DG) method for the ideal multi-ion magneto-hydrodynamics (MHD) equations. We s…
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…
Haar-type stochastic Galerkin formulations for hyperbolic systems with Lipschitz continuous flux function
Stephan Gerster, Aleksey Sikstel, Giuseppe Visconti
This work is devoted to the Galerkin projection of highly nonlinear random quantities. The dependency on a random input is described by Haar-type wavelet systems. The classical Haa…