Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit k-dependency for $P_k$ finite elements in $W^{m,p}$ error
  estimates: application to probabilistic laws for accuracy analysis   We derive an explicit $k-$dependence in $W^{m,p}$ error estimates for $P_k$
Lagrange finite elements. Two laws of probability are established to measure
the relative accuracy between $P_{k_1}$ and $P_{k_2}$ finite elements ($k_1 <
k_2$) in terms of $W^{m,p}$-norms. We further prove a weak asymptotic relation
in $D'(R)$ between these probabilistic laws when difference $k_2-k_1$ goes to
infinity. Moreover, as expected, one finds that $P_{k_2}$ finite element is
{\em surely more accurate} than $P_{k_1}$, for sufficiently small values of the
mesh size $h$. Nevertheless, our results also highlight cases where $P_{k_1}$
is {\em more likely accurate} than $P_{k_2}$, 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.

31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an