Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp Error Bounds for Piecewise Polynomial Approximation: Revisit and
  Application to Elliptic PDE Eigenvalue Computation   In this paper, we revisit approximation properties of piecewise polynomial
spaces, which contain more than ${\cal P}_{r-1}$ but not ${\cal P}_r$. We
develop more accurate upper and lower error bounds that are sharper than those
used in literature. These new error bounds, especially the lower bounds are
particular useful to finite element methods. As an important application, we
establish sharp lower bounds of the discretization error for Laplace and
$2m$-th order elliptic eigenvalue problems in various finite element spaces
under shape regular triangulations, and investigate the asymptotic convergence
behavior for large numerical eigenvalue approximations.

12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con