A posteriori Error Estimates for Numerical Solutions to Hyperbolic Conservation Laws]]>

The Liouville equation, its extensions, and related optimal control problems]]>

This talk provides an introduction to the formulation and solution of optimal control problems governed by the Liouville equation and related models. The purpose of this framework is the design of robust controls to steer the motion of particles, pedestrians, etc., where these agents are represented in terms of density functions. For this purpose, expected-value cost functionals are considered that include attracting potentials and different costs of the controls, whereas the control mechanism in the governing models is part of the drift or is included in a collision term.

In this talk, theoretical and numerical results concerning ensemble optimal control problems with Liouville, Fokker-Planck and linear Boltzmann equations are presented.

For further information about the seminar, please visit this webpage.

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Strong Convergence and adaptive timestepping for an SPDE]]>

Uniqueness and global convergence for a discretized inverse coefficient problem]]>

We then demonstrate that this result can be used to prove uniqueness, stability and global convergence for an inverse coefficient problem with finitely many measurements. We consider the problem of determining an unknown inverse Robin transmission coefficient in an elliptic PDE. Using a relation to monotonicity and localized potentials techniques, we show that a piecewise-constant coefficient on an a-priori known partition with a-priori known bounds is uniquely determined by finitely many boundary measurements and that it can be uniquely and stably reconstructed by a globally convergent Newton iteration. We derive a constructive method to identify these boundary measurements, calculate the stability constant and give a numerical example.

For further information about the seminar, please visit this webpage.