8 papers
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…
Rosenbrock-Wanner Methods: Construction and Mission
Jens Lang
This paper is concerned with the history of Rosenbrock-Wanner methods first initiated by Rosenbrock in 1963. His original ideas are highlighted and the main developments over 56 ye…
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…
A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data
Jens Lang, Robert Scheichl, David Silvester
We propose and analyse a fully adaptive strategy for solving elliptic PDEs with random data in this work. A hierarchical sequence of adaptive mesh refinements for the spatial appro…