Boundary elements with mesh refinements for the wave equation

Heiko Gimperlein, Fabian Meyer, Ceyhun Özdemir, David Stark, Ernst P. Stephan

Research output: Contribution to journalArticle

7 Citations (Scopus)
58 Downloads (Pure)

Abstract

The solution of the wave equation in a polyhedral domain in R3 admits an asymptotic singular expansion in a neighborhood of the corners and edges. In this article we formulate boundary and screen problems for the wave equation as equivalent boundary integral equations in time domain, study the regularity properties of their solutions and the numerical approximation. Guided by the theory for elliptic equations, graded meshes are shown to recover the optimal approximation rates known for smooth solutions. Numerical experiments illustrate the theory for screen problems. In particular, we discuss the Dirichlet and Neumann problems, as well as the Dirichlet-to-Neumann operator and applications to the sound emission of tires.
Original languageEnglish
Pages (from-to)867-912
Number of pages46
JournalNumerische Mathematik
Volume139
Issue number4
Early online date20 Feb 2018
DOIs
Publication statusPublished - Aug 2018

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