Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical analysis for time-dependent advection-diffusion problems with
  random discontinuous coefficients   Subsurface flows are commonly modeled by advection-diffusion equations.
Insufficient measurements or uncertain material procurement may be accounted
for by random coefficients. To represent, for example, transitions in
heterogeneous media, the parameters of the equation are spatially
discontinuous. Specifically, a scenario with coupled advection- and diffusion
coefficients that are modeled as sums of continuous random fields and
discontinuous jump components are considered. For the numerical approximation
of the solution, an adaptive, pathwise discretization scheme based on a Finite
Element approach is introduced. To stabilize the numerical approximation and
accelerate convergence, the discrete space-time grid is chosen with respect to
the varying discontinuities in each sample of the coefficients, leading to a
stochastic formulation of the Galerkin projection and the Finite Element basis.

29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int