Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A finite element method for elliptic problems with observational
  boundary data   In this paper we propose a finite element method for solving elliptic
equations with the observational Dirichlet boundary data which may subject to
random noises. The method is based on the weak formulation of Lagrangian
multiplier. We show the convergence of the random finite element error in
expectation and, when the noise is sub-Gaussian, in the Orlicz 2- norm which
implies the probability that the finite element error estimates are violated
decays exponentially. Numerical examples are included.

15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph