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Space-time discretization methods are becoming increasingly popular, since they allow adaptivity in space and time simultaneously, and can use parallel iterative solution strategies for time-dependent problems. However, in order to exploit these advantages, one needs to have a complete numerical analysis of the corresponding Galerkin methods.
Different strategies have been used to derive variational methods for the time domain boundary integral equations for the wave equation. The more established and successful ones include weak formulations based on the Laplace transform, and also time-space energetic variational formulations. However, their corresponding numerical analyses are still incomplete and present difficulties that are hard to overcome, if possible at all.
As an alternative, we pursue a new approach to formulate the boundary integral equations for the wave equation. The resulting mathematical formulation allows us to prove that the associated boundary integral operators are continuous and satisfy inf-sup conditions in trace spaces of the same regularity, which are closely related to standard energy spaces with the expected regularity in space and time. This feature is crucial from a numerical perspective, as it provides the foundations to derive sharper error estimates and paves the way to devise efficient adaptive space-time boundary element methods.
In this talk, I will give a short introduction to boundary element methods; briefly explain the current formulations for the wave equation; and finally discuss the new approach.


06. Dezember 2021, 13:00-14:00




FB Mathematik, AG Numerik und wissenschaftliches Rechnen




Mathematik, Numerik