The Highest Superconvergence Analysis of ADG Method for Two Point Boundary Values Problem

In this paper, an averaging discontinuous Galerkin (ADG) method for two point boundary value problems is analyzed. We prove, for any even polynomial degree k , the numerical flux convergence at a rate of 2 k + 2 for all mesh nodes (in particular, the numerical flux for k = 0 has the second order sup...

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Bibliographic Details
Published in:Journal of scientific computing 2017, Vol.70 (1), p.175-191
Main Authors: Wang, Jiangxing, Chen, Chuanmiao, Xie, Ziqing
Format: Article
Language:English
Subjects:
Algorithms
Boundary value problems
Computational Mathematics and Numerical Analysis
Equality
Estimates
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Polynomials
Theoretical
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Summary:In this paper, an averaging discontinuous Galerkin (ADG) method for two point boundary value problems is analyzed. We prove, for any even polynomial degree k , the numerical flux convergence at a rate of 2 k + 2 for all mesh nodes (in particular, the numerical flux for k = 0 has the second order superconvergence rate). Numerical experiments are shown to demonstrate the theoretical results.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-016-0247-0