Plane Wave Discontinuous Galerkin Methods: Exponential Convergence of the $$hp$$ h p -Version
نویسندگان
چکیده
منابع مشابه
Plane Wave Discontinuous Galerkin Methods
Standard low order Lagrangian finite element discretization of boundary value problems for the Helmholtz equation −∆u−ωu = f are afflicted with the so-called pollution phenomenon: though for sufficiently small hω an accurate approximation of u is possible, the Galerkin procedure fails to provide it. Attempts to remedy this have focused on incorporating extra information in the form of plane wav...
متن کاملPlane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the p-Version
Plane wave discontinuous Galerkin (PWDG) methods are a class of Trefftz-type methods for the spatial discretization of boundary value problems for the Helmholtz operator −∆− ω, ω > 0. They include the so-called ultra weak variational formulation from [O. Cessenat and B. Després, SIAM J. Numer. Anal., 35 (1998), pp. 255–299]. This paper is concerned with the a priori convergence analysis of PWDG...
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Thc devclopment of hp·version discontinuous Galerkin methods for hyperholic conservalion laws is presented in this work. A priori error estimates are dcrived for a model class of linear hyperbolic conservation laws. These estimates arc obtained using a ncw mesh-dependcnt norm that rel1ects thc dependcnce of the approximate solution on thc local element size and the local order of approximation....
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We establish the well-posedness of an hp-version time-stepping discontinuous Galerkin (DG) method for the numerical solution of fractional super-diffusion evolution problems. In particular, we prove the existence and uniqueness of approximate solutions for generic hp-version finite element spaces featuring non-uniform time-steps and variable approximation degrees. We then derive new hp-version ...
متن کاملPlane Wave Discontinuous Galerkin Methods : Analysis of The
We are concerned with a finite element approximation for time-harmonic wave propagation governed by the Helmholtz equation. The usually oscillatory behavior of solutions, along with numerical dispersion, render standard finite element methods grossly inefficient already in medium-frequency regimes. As an alternative, methods that incorporate information about the solution in the form of plane w...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2015
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-015-9260-1