Optimally adapted meshes for finite elements of arbitrary order and W 1, p norms

@article{Mirebeau2012OptimallyAM,
  title={Optimally adapted meshes for finite elements of arbitrary order and W 1, p  norms},
  author={Jean-Marie Mirebeau},
  journal={Numerische Mathematik},
  year={2012},
  volume={120},
  pages={271-305}
}
Given a function f defined on a bounded polygonal domain Ω ⊂ IR and a numberN > 0, we study the properties of the triangulation TN that minimizes the distance between f and its interpolation on the associated finite element space, over all triangulations of at most N elements. The error is studied in the W 1,p semi-norm for 1 ≤ p < ∞, and we consider Lagrange finite elements of arbitrary polynomial order m−1. We establish sharp asymptotic error estimates as N → +∞ when the optimal anisotropic… CONTINUE READING

Citations

Publications citing this paper.
Showing 1-10 of 17 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 22 references

Optimal meshes for finite elements of arbitrary order, Constructive Approximation

  • J.-M. Mirebeau
  • Vol 32
  • 2010
Highly Influential
10 Excerpts

On Asymptotical Behavior of the Optimal Linear Spline Interpolation Error of C2

  • V. Babenko, Y. Babenko, A. Ligun, A. Shumeiko
  • Functions, East J. Approx
  • 2006
Highly Influential
5 Excerpts

The optimal aspect ratio for piecewise quadratic anisotropic finite element approximation, proceedings of the conference

  • J.-M. Mirebeau
  • SampTA
  • 2011
1 Excerpt

Mirebeau, Sharp asymptotics of the Lp approximation error for interpolation on block partitions

  • Y. Babenko, T. Leskevich, J.-M
  • Numerische Mathematik,
  • 2010
1 Excerpt

Mirebeau, Adaptive and anisotropic piecewise polynomial approximation, chapter 4 of the book Multiscale

  • A. Cohen, J.-M
  • Nonlinear and Adaptive Approximation,
  • 2009
2 Excerpts

Similar Papers

Loading similar papers…