Abstract
We derive an explicit k-dependence in error estimates for
Lagrange finite elements. Two laws of probability are established to measure the relative accuracy between
and
finite elements, (
), in terms of
-norms. We further prove a weak asymptotic relation in
between these probabilistic laws when difference
goes to infinity. Moreover, as expected, one finds that
finite element is surely more accurate than
, for sufficiently small values of the mesh size h. Nevertheless, our results also highlight cases where
is more likely accurate than
, for a range of values of h. Hence, this approach brings a new perspective on how to compare two finite elements, which is not limited to the rate of convergence.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Joël Chaskalovic http://orcid.org/0000-0003-1263-5313
Notes
1 The space of functions locally integrable for any compact K of .