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Abstract
We consider solving the soundsoft scattering problem for the Helmholtz equation with the \(h\)version of the boundary element method using the standard secondkind combinedfield integral equations. We obtain sufficient conditions for the relative best approximation error to be bounded independently of \(k\). For certain geometries, these rigorously justify the commonlyheld belief that a fixed number of degrees of freedom per wavelength is sufficient to keep the relative best approximation error bounded independently of \(k\). We then obtain sufficient conditions for the Galerkin method to be quasioptimal, with the constant of quasioptimality independent of \(k\). Numerical experiments indicate that, while these conditions for quasioptimality are sufficient, they are not necessary for many geometries.
Original language  English 

Pages (fromto)  171214 
Number of pages  44 
Journal  BIT Numerical Mathematics 
Volume  55 
Issue number  1 
Early online date  4 Sept 2014 
DOIs  
Publication status  Published  Mar 2015 
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Dive into the research topics of 'When is the error in the hBEM for solving the Helmholtz equation bounded independently of k ?'. Together they form a unique fingerprint.Projects
 2 Finished

Post Doc Fellowship  New Methods and Analysis for Wave Propagation Problems
Engineering and Physical Sciences Research Council
1/04/11 → 31/03/14
Project: Research council

Boundary Integral Equation Methods for HF Scattering Problems
Graham, I. & Smyshlyaev, V. P.
Engineering and Physical Sciences Research Council
24/03/09 → 23/09/12
Project: Research council