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

Journal Article · · Journal of Scientific Computing
 [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)
+ Show Author Affiliations

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.

Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1330547
Journal Information:
Journal of Scientific Computing, Journal Name: Journal of Scientific Computing; ISSN 0885-7474
Publisher:
SpringerCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 7 works
Citation information provided by
Web of Science

References (18)

Finite element methods for elliptic equations using nonconforming elements journal January 1977
The Mathematical Theory of Finite Element Methods book January 2008
A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems journal January 2001
A discontinuous hp finite element method for convection—diffusion problems journal July 1999
A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier–Stokes Equations journal March 1997
Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems journal September 2001
A Modified Finite Volume Approximation of Second-Order Elliptic Equations with Discontinuous Coefficients journal January 2001
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems journal January 2002
A DiscontinuoushpFinite Element Method for Diffusion Problems journal November 1998
A weak Galerkin finite element method for second-order elliptic problems journal March 2013
An Interior Penalty Finite Element Method with Discontinuous Elements journal August 1982
A New Nonsymmetric Discontinuous Galerkin Method for Time Dependent Convection Diffusion Equations journal September 2012
Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems journal January 2009
A New Direct Discontinuous Galerkin Method with Symmetric Structure for Nonlinear Diffusion Equations journal June 2013
Two families of mixed finite elements for second order elliptic problems journal June 1985
An Elliptic Collocation-Finite Element Method with Interior Penalties journal February 1978
Nodal Discontinuous Galerkin Methods book December 2007
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems journal December 1998

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
discontinuous Galerkin method
second order elliptic problem