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

  title={Optimally adapted meshes for finite elements of arbitrary order and W 1, p  norms},
  author={Jean-Marie Mirebeau},
  journal={Numerische Mathematik},
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


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