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SUMMARY:Geometry-conforming discretizations of fractal domains - David Hew
 ett (University College London)
DTSTART:20260414T091500Z
DTEND:20260414T101500Z
UID:TALK243994@talks.cam.ac.uk
DESCRIPTION:Our focus is on the accurate numerical solution of PDEs and re
 lated spectral problems in domains with highly non-smooth (e.g. fractal) b
 oundary. For such problems\, an obvious approach is to first replace the d
 omain by a smoother "prefractal" approximation\, then apply a classical di
 scretization\, such as a conforming finite element method (FEM) on a simpl
 icial mesh. However\, a drawback of this approach is that to minimise the 
 effect of geometry-related approximation errors one needs a highly accurat
 e prefractal approximation\, which generally leads to extremely complicate
 d FEM meshes with a large number of elements. In this talk we present a no
 vel class of geometry-conforming FEM-type discretizations in which the fra
 ctal domain is meshed exactly using a finite number of non-simplicial elem
 ents which themselves have fractal boundary. As we shall demonstrate\, whi
 le such meshes cannot be used in the context of classical conforming FEM\,
  they can be successfully applied in the context of both (i) discontinuous
  Galerkin FEM and (ii) integral equation methods\, offering significantly 
 more efficient approximation than comparable prefractal-based methods. &nb
 sp\;\nThis is joint work with Andrea Moiola (Pavia)\, Sergio Gomez (Milano
  Bicocca)\, Joshua Bannister (UCL) and Andrew Gibbs (UCL).
LOCATION:Seminar Room 1\, Newton Institute
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