Skip to main content
Log in

Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I

  • Published:
Computational Geosciences Aims and scope Submit manuscript

Abstract

Three Galerkin methods using discontinuous approximation spaces are introduced to solve elliptic problems. The underlying bilinear form for all three methods is the same and is nonsymmetric. In one case, a penalty is added to the form and in another, a constraint on jumps on each face of the triangulation. All three methods are locally conservative and the third one is not restricted. Optimal a priori hp error estimates are derived for all three procedures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D.N. Arnold, An interior penalty finite element method with discontinuous elements, SIAM J. Numer. Anal. 19(4) (1982) 742–760.

    Article  MATH  MathSciNet  Google Scholar 

  2. I. Babuška and M. Suri, The h-p version of the finite element method with quasiuniform meshes, Math. Modeling Numer. Anal. 21(2) (1987) 199–238.

    Google Scholar 

  3. I. Babuška and M. Suri, The optimal convergence rates of the p version of the finite element method, SIAM J. Numer. Anal. 24(4) (1987).

  4. C.E. Baumann, An h-p adaptive discontinuous finite element method for computational fluid dynamics, Ph.D. thesis, The University of Texas at Austin (1997).

  5. J. Douglas and T. Dupont, Interior penalty procedures for elliptic and parabolic Galerkin methods, Lecture Notes in Physics, Vol. 58 (1976) pp. 207–216.

  6. J.T. Oden, I. Babuška and C.E. Baumann, A discontinous hp finite element method for diffusion problems, J. Comput. Phys. 146 (1998) 491–519.

    Article  MATH  MathSciNet  Google Scholar 

  7. P. Percell and M.F. Wheeler, A local residual finite element procedure for elliptic equations, SIAM J. Numer. Anal. 15(4) (1978) 705–714.

    Article  MATH  MathSciNet  Google Scholar 

  8. M.F. Wheeler, An elliptic collocation-finite element method with interior penalties, SIAM J. Numer. Anal. 15(1) (1978) 152–161.

    Article  MATH  MathSciNet  Google Scholar 

  9. M.F. Wheeler and B.L. Darlow, Interior penalty Galerkin procedures for miscible displacement problems in porous media, Comput. Methods Nonlinear Mech. (1980) 485–506.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rivière, B., Wheeler, M.F. & Girault, V. Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I. Computational Geosciences 3, 337–360 (1999). https://doi.org/10.1023/A:1011591328604

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1011591328604

Navigation