Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence and optimality of the adaptive nonconforming linear element
  method for the Stokes problem   In this paper, we analyze the convergence and optimality of a standard
adaptive nonconforming linear element method for the Stokes problem. After
establishing a special quasi--orthogonality property for both the velocity and
the pressure in this saddle point problem, we introduce a new prolongation
operator to carry through the discrete reliability analysis for the error
estimator. We then use a specially defined interpolation operator to prove
that, up to oscillation, the error can be bounded by the approximation error
within a properly defined nonlinear approximate class. Finally, by introducing
a new parameter-dependent error estimator, we prove the convergence and
optimality estimates.

13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci