A Class of Discontinuous Petrov-Galerkin Methods . Part III : Adaptivity

@inproceedings{Demkowicz2010ACO,
  title={A Class of Discontinuous Petrov-Galerkin Methods . Part III : Adaptivity},
  author={Leszek F. Demkowicz and Jay Gopalakrishnan and Antti H. Niemi},
  year={2010}
}
We continue our theoretical and numerical study on the Discontinuous Petrov-Galerkin method with optimal test functions in context of 1D and 2D convection-dominated diffusion problems and hp-adaptivity. With a proper choice of the norm for the test space, we prove robustness (uniform stability with respect to the diffusion parameter) and mesh-independence of the energy norm of the FE error for the 1D problem. With hp-adaptivity and a proper scaling of the norms for the test functions, we… CONTINUE READING
23 Citations
19 References
Similar Papers

Citations

Publications citing this paper.
Showing 1-10 of 23 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 19 references

A class of discontinuous Petrov-Galerkin methods. Part I: The transport equation, Comput

  • L. Demkowicz, J. Gopalakrishnan
  • Methods Appl. Mech. Engrg.Accepted, see also ICES…
  • 2009
Highly Influential
4 Excerpts

hp-Finite Element Methods for Singular Perturbations

  • J. Melenk
  • Springer, Berlin
  • 2002
Highly Influential
2 Excerpts

A class of Discontinuous Petrov–Galerkin methods

  • J. Chan, L. Demkowicz, R. Moser, N. Roberts
  • Part V: Solution of 1d Burgers and Navier–Stokes…
  • 2010
1 Excerpt

Analysis of the DPG method for the Poisson problem

  • L. Demkowicz, J. Gopalakrishnan
  • Tech. Rep. 37, ICES, submitteed to SIAM J. Num…
  • 2010
3 Excerpts

Applied Functional Analysis for Science and Engineering

  • J. Oden, L. Demkowicz
  • Chapman & Hall/CRC Press, Boca Raton
  • 2010

Schötzau

  • I. Zhu
  • A robust a posteriori error estimate for hp…
  • 2010
2 Excerpts

Robust Numerical Methods for Singularly Perturbed Differential Equations

  • H.-G. Roos, M. Stynes, L. Tobiska
  • 2nd Edition, Vol. 24 of Springer Series in…
  • 2008
2 Excerpts

Similar Papers

Loading similar papers…