When is the error in the $$h$$ h -BEM for solving the Helmholtz equation bounded independently of $$k$$ k ?
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| 024 | 7 | 0 | |a 10.1007/s10543-014-0501-5 |2 doi |
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| 245 | 0 | 0 | |a When is the error in the $$h$$ h -BEM for solving the Helmholtz equation bounded independently of $$k$$ k ? |h [Elektronische Daten] |c [I. Graham, M. Löhndorf, J. Melenk, E. Spence] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer Science+Business Media Dordrecht, 2014 | ||
| 690 | 7 | |a Helmholtz equation |2 nationallicence | |
| 690 | 7 | |a High frequency |2 nationallicence | |
| 690 | 7 | |a Boundary integral equation |2 nationallicence | |
| 690 | 7 | |a Boundary element method |2 nationallicence | |
| 690 | 7 | |a Pollution effect |2 nationallicence | |
| 700 | 1 | |a Graham |D I. |u Department of Mathematical Sciences, University of Bath, BA27, Bath, AY, UK |4 aut | |
| 700 | 1 | |a Löhndorf |D M. |u Kapsch TrafficCom, Am Europlatz 2, 1120, Wien, Austria |4 aut | |
| 700 | 1 | |a Melenk |D J. |u Institut für Analysis und Scientific Computing, Technische Universität Wien, 1040, Wien, Austria |4 aut | |
| 700 | 1 | |a Spence |D E. |u Department of Mathematical Sciences, University of Bath, BA27, Bath, AY, UK |4 aut | |
| 773 | 0 | |t BIT Numerical Mathematics |d Springer Netherlands |g 55/1(2015-03-01), 171-214 |x 0006-3835 |q 55:1<171 |1 2015 |2 55 |o 10543 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10543-014-0501-5 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10543-014-0501-5 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Graham |D I. |u Department of Mathematical Sciences, University of Bath, BA27, Bath, AY, UK |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Löhndorf |D M. |u Kapsch TrafficCom, Am Europlatz 2, 1120, Wien, Austria |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Melenk |D J. |u Institut für Analysis und Scientific Computing, Technische Universität Wien, 1040, Wien, Austria |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Spence |D E. |u Department of Mathematical Sciences, University of Bath, BA27, Bath, AY, UK |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t BIT Numerical Mathematics |d Springer Netherlands |g 55/1(2015-03-01), 171-214 |x 0006-3835 |q 55:1<171 |1 2015 |2 55 |o 10543 | ||