caa a22 4500 605496846 CHVBK 20210128100538.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s10543-014-0501-5 doi (NATIONALLICENCE)springer-10.1007/s10543-014-0501-5 When is the error in the $$h$$ h -BEM for solving the Helmholtz equation bounded independently of $$k$$ k ? [Elektronische Daten] [I. Graham, M. Löhndorf, J. Melenk, E. Spence] We consider solving the sound-soft scattering problem for the Helmholtz equation with the $$h$$ h -version of the boundary element method using the standard second-kind combined-field integral equations. We obtain sufficient conditions for the relative best approximation error to be bounded independently of $$k$$ k . For certain geometries, these rigorously justify the commonly-held belief that a fixed number of degrees of freedom per wavelength is sufficient to keep the relative best approximation error bounded independently of $$k$$ k . We then obtain sufficient conditions for the Galerkin method to be quasi-optimal, with the constant of quasi-optimality independent of $$k$$ k . Numerical experiments indicate that, while these conditions for quasi-optimality are sufficient, they are not necessary for many geometries. Springer Science+Business Media Dordrecht, 2014 Helmholtz equation nationallicence High frequency nationallicence Boundary integral equation nationallicence Boundary element method nationallicence Pollution effect nationallicence Graham I. Department of Mathematical Sciences, University of Bath, BA27, Bath, AY, UK aut Löhndorf M. Kapsch TrafficCom, Am Europlatz 2, 1120, Wien, Austria aut Melenk J. Institut für Analysis und Scientific Computing, Technische Universität Wien, 1040, Wien, Austria aut Spence E. Department of Mathematical Sciences, University of Bath, BA27, Bath, AY, UK aut BIT Numerical Mathematics Springer Netherlands 55/1(2015-03-01), 171-214 0006-3835 55:1<171 2015 55 10543 https://doi.org/10.1007/s10543-014-0501-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0501-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Graham I. Department of Mathematical Sciences, University of Bath, BA27, Bath, AY, UK aut NATIONALLICENCE 700 1- Löhndorf M. Kapsch TrafficCom, Am Europlatz 2, 1120, Wien, Austria aut NATIONALLICENCE 700 1- Melenk J. Institut für Analysis und Scientific Computing, Technische Universität Wien, 1040, Wien, Austria aut NATIONALLICENCE 700 1- Spence E. Department of Mathematical Sciences, University of Bath, BA27, Bath, AY, UK aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/1(2015-03-01), 171-214 0006-3835 55:1<171 2015 55 10543