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Journal of Scientific Computing
Published in: Journal of Scientific Computing 1/2016

23-07-2015

Preasymptotic Error Analysis of High Order Interior Penalty Discontinuous Galerkin Methods for the Helmholtz Equation with High Wave Number

Authors: Yu Du, Lingxue Zhu

Published in: Journal of Scientific Computing | Issue 1/2016

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Abstract

A preasymptotic error analysis of the interior penalty discontinuous Galerkin (IPDG) method of high order for Helmholtz equation with the first order absorbing boundary condition in two and three dimensions is proposed. We derive the \(H^1\)- and \(L^2\)- error estimates with explicit dependence on the wave number k. In particular, it is shown that if \(k(kh)^{2p}\) is sufficiently small, then the pollution errors of IPDG method in \(H^1\)-norm are bounded by \(O(k(kh)^{2p})\), which coincides with the phase error of the finite element method obtained by existent dispersion analyses on Cartesian grids, where h is the mesh size, p is the order of the approximation space and is fixed. Numerical tests are provided to verify the theoretical findings and to illustrate great capability of the symmetric IPDG method in reducing the pollution effect.
previous article Removing Mixture of Gaussian and Impulse Noise by Patch-Based Weighted Means
next article Pointwise Error Estimates and Two-Grid Algorithms of Discontinuous Galerkin Method for Strongly Nonlinear Elliptic Problems

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Metadata
Title
Preasymptotic Error Analysis of High Order Interior Penalty Discontinuous Galerkin Methods for the Helmholtz Equation with High Wave Number
Authors
Yu Du
Lingxue Zhu
Publication date
23-07-2015
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 1/2016
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-015-0074-8

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