9 papers · 1 filter
Adaptive Single- and Multilevel Stochastic Collocation Methods for Uncertain Gas Transport in Large-Scale Networks
Jens Lang, Pia Domschke, Elisa Strauch
In this paper, we are concerned with the quantification of uncertainties that arise from intra-day oscillations in the demand for natural gas transported through large-scale networ…
Well-Balanced and Asymptotic Preserving IMEX-Peer Methods
Moritz Schneider, Jens Lang
Peer methods are a comprehensive class of time integrators offering numerous degrees of freedom in their coefficient matrices that can be used to ensure advantageous properties, e.…
A Third-Order Weighted Essentially Non-Oscillatory Scheme in Optimal Control Problems Governed by Nonlinear Hyperbolic Conservation Laws
David Frenzel, Jens Lang
The weighted essentially non-oscillatory (WENO) methods are popular and effective spatial discretization methods for nonlinear hyperbolic partial differential equations. Although t…
Discrete Adjoint Implicit Peer Methods in Optimal Control
Jens Lang, Bernhard A. Schmitt
It is well known that in the first-discretize-then-optimize approach in the control of ordinary differential equations the adjoint method may converge under additional order condit…
Stability of explicit Runge-Kutta methods for high order finite element approximation of linear parabolic equations
Weizhang Huang, Lennard Kamenski, Jens Lang
We study the stability of explicit Runge-Kutta methods for high order Lagrangian finite element approximation of linear parabolic equations and establish bounds on the largest eige…
A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates
Weizhang Huang, Lennard Kamenski, Jens Lang
A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform on…