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We present a wavenumber-explicit convergence analysis of the hp finite element method applied to a class of heterogeneous Helmholtz problems with piecewise analytic coefficients at large wavenumber $k$.
Scattering theory
P.D. Lax and R.S. Phillips · 1964
Earlier work this paper cites.
Singular integrals and differentiability properties of functions
E.M. Stein · 1970
Earlier work this paper cites.
An observation concerning Ritz-Galerkin methods with indefinite bilinear forms
A.H. Schatz · 1974
Earlier work this paper cites.
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R. Melrose · 1975
Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Frank Ihlenburg · 1998
Earlier work this paper cites.
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Earlier work this paper cites.
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