Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A class of Galerkin schemes for time-dependent radiative transfer   The numerical solution of time-dependent radiative transfer problems is
challenging, both, due to the high dimension as well as the anisotropic
structure of the underlying integro-partial differential equation. In this
paper we propose a general framework for designing numerical methods for
time-dependent radiative transfer based on a Galerkin discretization in space
and angle combined with appropriate time stepping schemes. This allows us to
systematically incorporate boundary conditions and to preserve basic properties
like exponential stability and decay to equilibrium also on the discrete level.
We present the basic a-priori error analysis and provide abstract error
estimates that cover a wide class of methods. The starting point for our
considerations is to rewrite the radiative transfer problem as a system of
evolution equations which has a similar structure like first order hyperbolic
systems in acoustics or electrodynamics. This analogy allows us to generalize
the main arguments of the numerical analysis for such applications to the
radiative transfer problem under investigation. We also discuss a particular
discretization scheme based on a truncated spherical harmonic expansion in
angle, a finite element discretization in space, and the implicit Euler method
in time. The performance of the resulting mixed PN-finite element time stepping
scheme is demonstrated by computational results.

7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an