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SUMMARY:Is the FEM error smaller away from the scatterer than near it for 
 high-frequency Helmholtz problems with trapping? - Euan Spence (University
  of Bath)
DTSTART:20230418T151500Z
DTEND:20230418T160000Z
UID:TALK198724@talks.cam.ac.uk
DESCRIPTION:Studying the local behaviour of the FEM error goes back to Nit
 sche and Schatz in 1974\, and this behaviour is particularly important for
  scattering problems\, since the far-field pattern can be obtained from kn
 owing 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 &ldquo\;y
 es&rdquo\; &ndash\; with the error away an algebraic factor of k smaller t
 han the error near &ndash\; when the data is such that the solution "sees"
  the trapping (in the sense that the ratio between the norm of the solutio
 n and the norm of the data is larger\, as a function of frequency\, than i
 t would be for a nontrapping problem). This is joint work with Martin Aver
 seng (Bath) and Jeff Galkowski (UCL).
LOCATION:Seminar Room 1\, Newton Institute
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