skip to main content

DOE PAGESDOE PAGES

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

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:
Grant/Contract Number:
AC05-00OR22725
Type:
Accepted Manuscript
Journal Name:
Journal of Scientific Computing
Additional Journal Information:
Journal Name: Journal of Scientific Computing; Journal ID: ISSN 0885-7474
Publisher:
Springer
Research Org:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; discontinuous Galerkin method; second order elliptic problem
OSTI Identifier:
1330547