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Journal of Scientific Computing

Erschienen in:

14.05.2016

An Unconditionally Stable Discontinuous Galerkin Method for the Elastic Helmholtz Equations with Large Frequency

verfasst von: Xiaobing Feng, Cody Lorton

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2016

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Abstract

In this paper we propose and analyze an interior penalty discontinuous Galerkin (IP-DG) method using piecewise linear polynomials for the elastic Helmholtz equations with the first order absorbing boundary condition. It is proved that the sesquilinear form for the problem satisfies a generalized weak coercivity property, which immediately infers a stability estimate for the solution of the differential problem in all frequency regimes. It is also proved that the proposed IP-DG method is unconditionally stable with respect to both frequency \(\omega \) and mesh size h. Sub-optimal order (with respect to h) error estimates in the broken \(H^1\)-norm and in the \(L^2\)-norm are obtained in all mesh regimes. These estimate improve to optimal order when the mesh size h is restricted to the pre-asymptotic regime (i.e., \(\omega ^{\beta } h =O(1)\) for some \(1\le \beta <2\)). Numerical experiments are also presented to validate the theoretical results and to numerically examine the pollution effect (with respect to \(\omega \)) in the error bounds.

Vorheriger Artikel A Novel Solver for the Generalized Riemann Problem Based on a Simplified LeFloch–Raviart Expansion and a Local Space–Time Discontinuous Galerkin Formulation

Nächster Artikel Implicit Multistage Two-Derivative Discontinuous Galerkin Schemes for Viscous Conservation Laws

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Titel: An Unconditionally Stable Discontinuous Galerkin Method for the Elastic Helmholtz Equations with Large Frequency
verfasst von: Xiaobing Feng
Cody Lorton
Publikationsdatum: 14.05.2016
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-016-0219-4

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