.. DO NOT MODIFY: this file was automatically generated!

:orphan:

Seminar by Karsten Urban
=================================
.. container:: sd-badge-seminar-container

    :bdg-primary-line:`Speaker`

    .. container:: sd-badge-next-text

        Karsten Urban (Universität Ulm)

    :bdg-primary-line:`Title`

    .. container:: sd-badge-next-text

        A reduced basis method for the Schrödinger equation

    :bdg-primary-line:`Date`

    .. container:: sd-badge-next-text

        * March 14, 2023 16:00 CET+0100 (Europe/Rome)
        * March 14, 2023 11:00 EDT-0400 (US/Eastern)
        * March 14, 2023 10:00 CDT-0500 (US/Central)
        * March 14, 2023 08:00 PDT-0700 (US/Pacific)

    :bdg-primary-line:`Abstract`

    .. container:: sd-badge-next-text

        We present a well-posed ultra-weak space-time variational formulation
        for the time-dependent version of the linear Schrödinger equation with
        an instationary Hamiltonian. We prove optimal inf-sup stability and
        introduce a space-time Petrov-Galerkin discretization with optimal
        discrete inf-sup stability.
        
        We show norm-preservation of the ultra-weak formulation. The inf-sup
        optimal Petrov-Galerkin discretization is shown to be asymptotically
        norm-preserving, where the deviation is shown to be in the order of the
        discretization. In addition, we introduce a Galerkin discretization,
        which has suboptimal inf-sup stability but exact norm-preservation.
        
        Numerical experiments underline the performance of the ultra-weak
        space-time variational formulation, especially for non-smooth initial
        data.

    :bdg-primary-line:`Recording`

    .. container:: sd-badge-next-text

        Watch the recording on `our YouTube channel <https://www.youtube.com/watch?v=F5qTAcqkP2k>`_.