A nonconforming domain decomposition approximation for the Helmholtz screen problem with hypersingular operator

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• 作者：Norbert Heuer and Gredy Salmeró ; n
• 刊名：Numerical Methods for Partial Differential Equations
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：33
• 期：1
• 页码：125-141
• 全文大小：1156K
• ISSN：1098-2426

文摘

We present and analyze a nonconforming domain decomposition approximation for a hypersingular operator governed by the Helmholtz equation in three dimensions. This operator appears when considering the corresponding Neumann problem in unbounded domains exterior to open surfaces. We consider small wave numbers and low-order approximations with Nitsche coupling across interfaces. Under appropriate assumptions on mapping properties of the weakly singular and hypersingular operators with Helmholtz kernel, we prove that this method converges almost quasioptimally, that is, with optimal orders reduced by an arbitrarily small positive number. Numerical experiments confirm our error estimate.