6 papers · 1 filter
A note on the convergence analysis of Laguerre approximations for analytic functions
Thomas Caussade, David P. Hewett
In a recent paper (H. Wang, Math. Comp. 93, 2861-2884, 2024), Wang has presented a number of results concerning the convergence of approximations based on generalised Laguerre poly…
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…
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…
Discontinuous piecewise polynomial approximation on non-Lipschitz domains
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…
Integral equation methods for acoustic scattering by fractals
A. M. Caetano, S. N. Chandler-Wilde, X. Claeys +3
We study sound-soft time-harmonic acoustic scattering by general scatterers, including fractal scatterers, in 2D and 3D space. For an arbitrary compact scatterer we reformulate…
Fast hybrid numerical-asymptotic boundary element methods for high frequency screen and aperture problems based on least-squares collocation
Andrew Gibbs, David Hewett, Daan Huybrechs +1
We present a hybrid numerical-asymptotic (HNA) boundary element method (BEM) for high frequency scattering by two-dimensional screens and apertures, whose computational cost to ach…