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Plane Wave Discontinuous Galerkin Methods: Exponential Convergence of the $$hp$$ h p -Version
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نویسنده
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Hiptmair R. ,Moiola A. ,Perugia I.
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منبع
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foundations of computational mathematics - 2016 - دوره : 16 - شماره : 3 - صفحه:637 -675
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چکیده
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We consider the two-dimensional helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. our discretisation relies on the trefftz-discontinuous galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. we prove exponential convergence of the discrete solution in terms of number of unknowns.
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کلیدواژه
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Helmholtz equation ,Approximation by plane waves ,Trefftz-discontinuous Galerkin method ,(hp)-version ,A priori convergence analysis ,Exponential convergence ,65N30 ,65N15 ,35J05
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آدرس
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Seminar of Applied Mathematics, ETH Zürich, Switzerland, University of Reading, Department of Mathematics and Statistics, UK, University of Vienna, Austria. University of Pavia, Department of Mathematics, Italy
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Authors
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