Skip to main content

Part of the book series: IUTAM BookSeries ((IUTAMBOOK,volume 11))

Abstract

We provide a brief overview of our recent work on applications of discontinuous Galerkin methods in solid mechanics. The discussion is light in technical details, and rather emphasizes key ideas, advantages and disadvantages of the approach, illustrating these with several numerical examples.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal., 39:1749–1779, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  2. D.N. Arnold, F. Brezzi, and L.D. Marini. A family of discontinuous Galerkin Finite Elements for the Reissner—Mindlin plate. Journal of Scientific Computing, 22(1):25–45, 2005.

    Article  MathSciNet  Google Scholar 

  3. A. Buffa and C. Ortner. Variational convergence of IP-DGFEM. Technical Report 07/10, Oxford University Computing Laboratory, Numerical Analysis Group, Wolfson Building, Parks Road, Oxford, England OX1 3QD, April 2007.

    Google Scholar 

  4. F. Celiker, B. Cockburn, and H.K. Stolarski. Locking-free optimal discontinuous Galerkin methods for Timoshenko beams. SIAM Journal on Numerical Analysis, 44:2297, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  5. B. Cockburn and C.W. Shu. Runge-Kutta discontinuous Galerkin methods for convectiondominated problems. J. Sci. Comput, 16(3):173–261, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  6. J.K. Djoko, F. Ebobisse, A.T. McBride, and B.D. Reddy. A discontinuous Galerkin formulation for classical and gradient plasticity — Part 1: Formulation and analysis. Computer Methods in Applied Mechanics and Engineering, 196(37–40):3881–3897, 2007.

    Article  MathSciNet  Google Scholar 

  7. J.K. Djoko, F. Ebobisse, A.T. McBride, and B.D. Reddy. A discontinuous Galerkin formulation for classical and gradient plasticity. Part 2: Algorithms and numerical analysis. Computer Methods in Applied Mechanics and Engineering, 197(1–4):1–21, 2007.

    Article  MathSciNet  Google Scholar 

  8. G. Engel, K. Garikipati, T.J.R. Hughes, M.G. Larson, L. Mazzei, and R.L. Taylor. Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, strain gradient elasticity. Computer Methods in Applied Mechanics and Engineering, 191:3669–3750, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  9. A. Ten Eyck and A. Lew. Discontinuous Galerkin methods for nonlinear elasticity. International Journal for Numerical Methods in Engineering, 67:1204–1243, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  10. S. Guzey, B. Cockburn, and H.K. Stolarski. The embedded discontinuous Galerkin method: Application to linear shell problems. International Journal for Numerical Methods in Engineering, 70:757–790, 2007.

    Article  MathSciNet  Google Scholar 

  11. P. Hansbo and M.G. Larson. Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche’s method. Computer Methods in Applied Mechanics and Engineering, 191(17):1895–1908, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  12. A. Lew and G. Buscaglia. A discontinuous-Galerkin-based immersed boundary method. International Journal for Numerical Methods in Engineering, 2008 (in press).

    Google Scholar 

  13. A. Lew, P. Neff, D. Sulsky, and M. Ortiz. Optimal BV estimates for a discontinuous Galerkin method in linear elasticity. Applied Mathematics Research Express, 3:73–106, 2004.

    Google Scholar 

  14. L. Noels and R. Radovitzky. A new discontinuous Galerkin method for Kirchhoff-Love shells. http://asap.mit.edu/publications/journal/cmame-2007.pdf, 2007.

  15. M. O’Connel and C. Taylor. Personal communication, 2007. Stanford University.

    Google Scholar 

  16. A. Ten Eyck, F. Celiker, and A. Lew. Adaptive stabilization of discontinuous Galerkin methods for nonlinear elasticity: Analytical estimates. Computer Methods in Applied Mechanics and Engineering, 197(33–40):2989–3000, 2008.

    Article  Google Scholar 

  17. A. Ten Eyck, F. Celiker, and A. Lew. Adaptive stabilization of discontinuous Galerkin methods for nonlinear elasticity: Motivation, formulation and numerical examples. Computer Methods in Applied Mechanics and Engineering, 2008 (in press).

    Google Scholar 

  18. G.N. Wells and N.T. Dung. A CO discontinuous Galerkin formulation for Kirchhoff plates. Computer Methods in Applied Mechanics and Engineering, 196(35–36):3370–3380, 2007.

    Article  MathSciNet  Google Scholar 

  19. G.N. Wells, E. Kuhl, and K. Garikipati. A discontinuous Galerkin method for the Cahn—Hilliard equation. Journal of Computational Physics, 218(2):860–877, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  20. T.P. Wihler. Locking-free DGFEM for elasticity problems in polygons. IMA Journal of Numerical Analysis, 24:45–75, 2004.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer Science+Business Media B.V

About this paper

Cite this paper

Lew, A., Ten Eyck, A., Rangarajan, R. (2008). Some Applications of Discontinuous Galerkin Methods in Solid Mechanics. In: Reddy, B.D. (eds) IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media. IUTAM BookSeries, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9090-5_21

Download citation

  • DOI: https://doi.org/10.1007/978-1-4020-9090-5_21

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-9089-9

  • Online ISBN: 978-1-4020-9090-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics