### TIME DOMAIN BOUNDARY ELEMENT METHODS FOR THE NEUMANN PROBLEM: ERROR ESTIMATES AND ACOUSTIC PROBLEMS

Heiko Gimperlein1, Ceyhun Özdemir2, Ernst P. Stephan2

1. 1. Maxwell Institute for Mathematical Sciences and Department of Mathematics, Heriot-Watt University, Edinburgh EH14;
4 AS, UK, and Institute for Mathematics, University of Paderborn, 33098 Paderborn, Germany;
2. Institute of Applied Mathematics, Leibniz University Hannover, 30167 Hannover, Germany
• Received:2016-01-04 Revised:2016-10-18 Online:2018-01-15 Published:2018-01-15
• Supported by:

Parts of this work were funded by BMWi under the project SPERoN 2020, part Ⅱ, Leiser Straßenverkehr, grant number 19 U 10016 F. H. G. acknowledges support by ERC Advanced Grant HARG 268105. C. O. is supported by a scholarship of the Avicenna foundation.

Heiko Gimperlein, Ceyhun Özdemir, Ernst P. Stephan. TIME DOMAIN BOUNDARY ELEMENT METHODS FOR THE NEUMANN PROBLEM: ERROR ESTIMATES AND ACOUSTIC PROBLEMS[J]. Journal of Computational Mathematics, 2018, 36(1): 70-89.

We investigate time domain boundary element methods for the wave equation in R3, with a view towards sound emission problems in computational acoustics. The Neumann problem is reduced to a time dependent integral equation for the hypersingular operator, and we present a priori and a posteriori error estimates for conforming Galerkin approximations in the more general case of a screen. Numerical experiments validate the convergence of our boundary element scheme and compare it with the numerical approximations obtained from an integral equation of the second kind. Computations in a half-space illustrate the influence of the reflection properties of a flat street.

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