An HDG Method with Orthogonal Projections in Facet Integrals

Issei Oikawa

Research output: Contribution to journalArticle

Abstract

We propose and analyze a new hybridizable discontinuous Galerkin (HDG) method for second-order elliptic problems. Our method is obtained by inserting the (Formula presented.)-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 (Formula presented.), (Formula presented.) 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.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalJournal of Scientific Computing
DOIs
Publication statusAccepted/In press - 2018 Jan 19

Fingerprint

Orthogonal Projection
Discontinuous Galerkin Method
Galerkin methods
Facet
Polynomials
Trace
Scalar
Second-order Elliptic Problems
Discontinuous Galerkin
Superconvergence
Order of Convergence
Post-processing
Non-negative
Verify
Imply
Numerical Results
Polynomial
Integer
Formulation

Keywords

  • Discontinuous Galerkin
  • Hybridization
  • Superconvergence

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Engineering(all)
  • Computational Theory and Mathematics

Cite this

An HDG Method with Orthogonal Projections in Facet Integrals. / Oikawa, Issei.

In: Journal of Scientific Computing, 19.01.2018, p. 1-11.

Research output: Contribution to journalArticle

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