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Title: Direct discontinuous Galerkin method and its variations for second order elliptic equations

Abstract

In this study, we study direct discontinuous Galerkin method (Liu and Yan in SIAM J Numer Anal 47(1):475–698, 2009) and its variations (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010; Vidden and Yan in J Comput Math 31(6):638–662, 2013; Yan in J Sci Comput 54(2–3):663–683, 2013) for 2nd order elliptic problems. A priori error estimate under energy norm is established for all four methods. Optimal error estimate under L 2 norm is obtained for DDG method with interface correction (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010) and symmetric DDG method (Vidden and Yan in J Comput Math 31(6):638–662, 2013). A series of numerical examples are carried out to illustrate the accuracy and capability of the schemes. Numerically we obtain optimal (k+1)th order convergence for DDG method with interface correction and symmetric DDG method on nonuniform and unstructured triangular meshes. An interface problem with discontinuous diffusion coefficients is investigated and optimal (k+1)th order accuracy is obtained. Peak solutions with sharp transitions are captured well. Highly oscillatory wave solutions of Helmholz equation are well resolved.

Authors:
 [1];  [2];  [3];  [2]
  1. Zhejiang Ocean Univ., Zhoushan (China); Key Lab. of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhoushan (China)
  2. Iowa State Univ., Ames, IA (United States)
  3. Shandong Jianzhu Univ., Jinan (China)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1330547
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Scientific Computing
Additional Journal Information:
Journal Name: Journal of Scientific Computing; Journal ID: ISSN 0885-7474
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; discontinuous Galerkin method; second order elliptic problem

Citation Formats

Huang, Hongying, Chen, Zheng, Li, Jin, and Yan, Jue. Direct discontinuous Galerkin method and its variations for second order elliptic equations. United States: N. p., 2016. Web. doi:10.1007/s10915-016-0264-z.
Huang, Hongying, Chen, Zheng, Li, Jin, & Yan, Jue. Direct discontinuous Galerkin method and its variations for second order elliptic equations. United States. doi:10.1007/s10915-016-0264-z.
Huang, Hongying, Chen, Zheng, Li, Jin, and Yan, Jue. Tue . "Direct discontinuous Galerkin method and its variations for second order elliptic equations". United States. doi:10.1007/s10915-016-0264-z. https://www.osti.gov/servlets/purl/1330547.
@article{osti_1330547,
title = {Direct discontinuous Galerkin method and its variations for second order elliptic equations},
author = {Huang, Hongying and Chen, Zheng and Li, Jin and Yan, Jue},
abstractNote = {In this study, we study direct discontinuous Galerkin method (Liu and Yan in SIAM J Numer Anal 47(1):475–698, 2009) and its variations (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010; Vidden and Yan in J Comput Math 31(6):638–662, 2013; Yan in J Sci Comput 54(2–3):663–683, 2013) for 2nd order elliptic problems. A priori error estimate under energy norm is established for all four methods. Optimal error estimate under L2 norm is obtained for DDG method with interface correction (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010) and symmetric DDG method (Vidden and Yan in J Comput Math 31(6):638–662, 2013). A series of numerical examples are carried out to illustrate the accuracy and capability of the schemes. Numerically we obtain optimal (k+1)th order convergence for DDG method with interface correction and symmetric DDG method on nonuniform and unstructured triangular meshes. An interface problem with discontinuous diffusion coefficients is investigated and optimal (k+1)th order accuracy is obtained. Peak solutions with sharp transitions are captured well. Highly oscillatory wave solutions of Helmholz equation are well resolved.},
doi = {10.1007/s10915-016-0264-z},
journal = {Journal of Scientific Computing},
number = ,
volume = ,
place = {United States},
year = {Tue Aug 23 00:00:00 EDT 2016},
month = {Tue Aug 23 00:00:00 EDT 2016}
}

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