Towards coercive boundary element methods for the wave equation
Olaf Steinbach (Graz University of Technology)
Carolina Urzúa–Torres (TU Delft - Numerical Analysis)
Marco Zank (University of Vienna)
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Abstract
We discuss the ellipticity of the single layer boundary integral operator for the wave equation in one space dimension. This result not only generalizes the well-known ellipticity of the energetic boundary integral formulation in L2, but it also turns out to be a particular case of a recent result on the inf-sup stability of boundary integral operators for the wave equation. Instead of the time derivative in the energetic formulation, we use a modified Hilbert transformation, which allows us to stay in Sobolev spaces of the same order.