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

Huang, Hongying; Chen, Zheng; Li, Jin; Yan, Jue

doi:10.1007/s10915-016-0264-z

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

Journal Article · Tue Aug 23 00:00:00 EDT 2016 · Journal of Scientific Computing

DOI:https://doi.org/10.1007/s10915-016-0264-z· OSTI ID:1330547

Huang, Hongying ^[1]; Chen, Zheng ^[2]; Li, Jin ^[3]; Yan, Jue ^[2]

Zhejiang Ocean Univ., Zhoushan (China); Key Lab. of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhoushan (China)
Iowa State Univ., Ames, IA (United States)
Shandong Jianzhu Univ., Jinan (China)

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.

View Accepted Manuscript (DOE)

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

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

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