Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiscale stabilization for convection-dominated diffusion in
  heterogeneous media   We develop a Petrov-Galerkin stabilization method for multiscale
convection-diffusion transport systems. Existing stabilization techniques add a
limited number of degrees of freedom in the form of bubble functions or a
modified diffusion, which may not sufficient to stabilize multiscale systems.
We seek a local reduced-order model for this kind of multiscale transport
problems and thus, develop a systematic approach for finding reduced-order
approximations of the solution. We start from a Petrov-Galerkin framework using
optimal weighting functions. We introduce an auxiliary variable to a mixed
formulation of the problem. The auxiliary variable stands for the optimal
weighting function. The problem reduces to finding a test space (a reduced
dimensional space for this auxiliary variable), which guarantees that the error
in the primal variable (representing the solution) is close to the projection
error of the full solution on the reduced dimensional space that approximates
the solution. To find the test space, we reformulate some recent mixed
Generalized Multiscale Finite Element Methods. We introduce snapshots and local
spectral problems that appropriately define local weight and trial spaces. In
particular, we use energy minimizing snapshots and local spectral
decompositions in the natural norm associated with the auxiliary variable. The
resulting spectral decomposition adaptively identifies and builds the optimal
multiscale space to stabilize the system. We discuss the stability and its
relation to the approximation property of the test space. We design online
basis functions, which accelerate convergence in the test space, and
consequently, improve stability. We present several numerical examples and show
that one needs a few test functions to achieve an error similar to the
projection error in the primal variable irrespective of the Peclet number.

18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas