Superconvergence of the local discontinuous Galerkin method for the linearized Korteweg-de Vries equation

被引：30

作者：

Hufford, Casey ^{[1
]}

Xing, Yulong ^{[1
,2
]}

机构：

[1] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

[2] Oak Ridge Natl Lab, Div Math & Comp Sci, Oak Ridge, TN 37831 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2014年 / 255卷

基金：

美国国家科学基金会;

关键词：

Local discontinuous Galerkin method; Korteweg-de Vries equation; Superconvergence; Error estimates; FINITE-ELEMENT-METHOD; ONE-DIMENSIONAL SYSTEMS; CONSERVATION-LAWS; UNSTRUCTURED GRIDS; VOLUME METHOD; FORMULATION;

D O I：

10.1016/j.cam.2013.06.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the superconvergence property of the local discontinuous Galerkin (LOG) method for solving the linearized Korteweg-de Vries (KdV) equation. We prove that, if the piecewise P-k polynomials with k >= 1 are used, the LDG solution converges to a particular projection of the exact solution with the order k + 3/2, when the upwind flux is used for the convection term and the alternating flux is used for the dispersive term. Numerical examples are provided at the end to support the theoretical results. Published by Elsevier B.V.

引用

页码：441 / 455

页数：15

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