Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence and optimality of the adaptive Morley element method   This paper is devoted to the convergence and optimality analysis of the
adaptive Morley element method for the fourth order elliptic problem. A new
technique is developed to establish a quasi-orthogonality which is crucial for
the convergence analysis of the adaptive nonconforming method. By introducing a
new parameter-dependent error estimator and further establishing a discrete
reliability property, sharp convergence and optimality estimates are then fully
proved for the fourth order elliptic problem.

1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
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The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con