Speaker
Carolina Urzua-Torres, TU Delft
Abstract
We present a novel framework for boundary integral equations for the wave equation. Unlike previous attempts, our mathematical formulation allows us to show 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. This property is crucial from a numerical point of view, as it establishes the foundations to derive sharper error estimates and paves the way to develop efficient adaptive space-time boundary element methods and stable space-time FEM/BEM coupling.
Moreover, the fact that the operators verify inf-sup conditions but not coercivity explains the instabilities that practitioners have observed in the past. It also tells us that stability of space-time BEM for the wave equation is guaranteed if we choose boundary element spaces such that the discrete inf-sup condition is uniformly satisfied. In this talk, I will give an overview of the new framework and summarize what we have learnt so far.