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Is the FEM error smaller away from the scatterer than near it for high-frequency Helmholtz problems with trapping?

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MWSW03 - Computational methods for multiple scattering

Studying the local behaviour of the FEM error goes back to Nitsche and Schatz in 1974, and this behaviour is particularly important for scattering problems, since the far-field pattern can be obtained from knowing the solution in any annulus around the scatterer. However, perhaps surprisingly, the question in the title seems not to have been rigorously investigated before. We show that the answer to the question is “yes” – with the error away an algebraic factor of k smaller than the error near – when the data is such that the solution “sees” the trapping (in the sense that the ratio between the norm of the solution and the norm of the data is larger, as a function of frequency, than it would be for a nontrapping problem). This is joint work with Martin Averseng (Bath) and Jeff Galkowski (UCL).

This talk is part of the Isaac Newton Institute Seminar Series series.

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