Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Posteriori Error Estimation and Adaptive Algorithm for the
  Atomistic/Continuum Coupling in 2D   Atomistic/continuum coupling methods aim to achieve optimal balance between
accuracy and efficiency. Adaptivity is the key for the efficient implementation
of such methods. In this paper, we carry out a rigorous a posteriori analysis
of the residual, the stability constant, and the error bound, for a consistent
atomistic/continuum coupling method in 2D. We design and implement the
corresponding adaptive mesh refinement algorithm, and the convergence rate with
respect to degrees of freedom is optimal compare with a priori error estimates.

12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph