Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computable error estimates for finite element approximations of elliptic
  partial differential equations with rough stochastic data   We derive computable error estimates for finite element approximations of
linear elliptic partial differential equations (PDE) with rough stochastic
coefficients. In this setting, the exact solutions contain high frequency
content that standard a posteriori error estimates fail to capture. We propose
goal-oriented estimates, based on local error indicators, for the pathwise
Galerkin and expected quadrature errors committed in standard, continuous,
piecewise linear finite element approximations. Derived using easily validated
assumptions, these novel estimates can be computed at a relatively low cost and
have applications to subsurface flow problems in geophysics where the
conductivities are assumed to have lognormal distributions with low regularity.
Our theory is supported by numerical experiments on test problems in one and
two dimensions.

16
The categories of this paper are: stat
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg