6 papers
Integral Equation Methods for Scattering by Multifractal Obstacles
Simon N. Chandler-Wilde, Gabriel Claret, David P. Hewett +2
Caetano et al. (Proc. R. Soc. A. 481:20230650, 2025) have proposed a formulation for sound-soft acoustic scattering by a compact scatterer O Rn, in which the scattered fi…
A discontinuous Galerkin method with fractal elements
Sergio Gómez, David Hewett, Andrea Moiola
We formulate, analyse, and implement a discontinuous Galerkin finite element method (DG-FEM) for the approximation of the solution of an elliptic boundary value problem in a domain…
Discontinuous piecewise polynomial approximation on non-Lipschitz domains
D P Hewett, David P Hewett
We prove best approximation error estimates for discontinuous piecewise polynomial approximation in fractional Sobolev spaces on non-Lipschitz meshes of non-Lipschitz domains. In p…
Acoustic scattering by fractal inhomogeneities via geometry-conforming Galerkin methods for the Lippmann-Schwinger equation
Joshua Bannister, David P. Hewett, Andrew Gibbs
We propose and analyse a numerical method for time-harmonic acoustic scattering in , , by a class of inhomogeneities (penetrable scatterers) with fractal bound…
Properties of IFS attractors with non-empty interiors, related rough domains, and associated function spaces and scattering problems
António Caetano, António Caetano, Simon N. Chandler-Wilde +1
We study fractal sets with non-empty interior , that are attractors of iterated function systems (IFSs) of contracting similarities satisfying the open s…
Kernels of trace operators via fine continuity
Michael Hinz, Simon N. Chandler-Wilde, David P. Hewett
Given a closed subset of that is the support of a measure , we study the kernels of trace operators from fractional Sobolev spaces in…