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A nonconforming domain decomposition approximation for the Helmholtz screen problem with hypersingular operator
Author(s) -
Heuer Norbert,
Salmerón Gredy
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22077
Subject(s) - mathematics , helmholtz equation , domain decomposition methods , operator (biology) , helmholtz free energy , mathematical analysis , domain (mathematical analysis) , differential operator , partial differential equation , kernel (algebra) , pure mathematics , finite element method , boundary value problem , biochemistry , chemistry , physics , repressor , quantum mechanics , gene , transcription factor , thermodynamics
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. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 125–141, 2017