An HDG Method with Orthogonal Projections in Facet Integrals

Journal of Scientific Computing volume 76, pages1044–1054(2018)Cite this article

Abstract

We propose and analyze a new hybridizable discontinuous Galerkin (HDG) method for second-order elliptic problems. Our method is obtained by inserting the \(L^2\)-orthogonal projection onto the approximate space for a numerical trace into all facet integrals in the usual HDG formulation. The orders of convergence for all variables are optimal if we use polynomials of degree \(k+l\), \(k+1\) and k, where k and l are any non-negative integers, to approximate the vector, scalar and trace variables, which implies that our method can achieve superconvergence for the scalar variable without postprocessing. Numerical results are presented to verify the theoretical results.

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Affiliations

  1. Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Issei Oikawa

Authors
  1. Issei Oikawa
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Correspondence to Issei Oikawa.

Additional information

This work was supported by JSPS KAKENHI Nos. 15H03635, 15K13454, 17K14243 and 17K18738.

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Oikawa, I. An HDG Method with Orthogonal Projections in Facet Integrals. J Sci Comput 76, 1044–1054 (2018). https://doi.org/10.1007/s10915-018-0648-3

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Keywords

  • Discontinuous Galerkin
  • Hybridization
  • Superconvergence

Mathematics Subject Classification

  • 65N12
  • 65N30