Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the TVD property of second order methods for 2D scalar conservation
  laws   The total variation diminishing (TVD) property is an important tool for
ensuring nonlinear stability and convergence of numerical solutions of
one-dimensional scalar conservation laws. However, it proved to be challenging
to extend this approach to two-dimensional problems. Using the anisotropic
definition for discrete total variation (TV), it was shown in \cite{Goodman}
that TVD solutions of two-dimensional hyperbolic equations are at most first
order accurate. We propose to use an alternative definition resulting from a
full discretization of the semi-discrete Raviart-Thomas TV. We demonstrate
numerically using the second order discontinuous Galerkin method that limited
solutions of two-dimensional hyperbolic equations are TVD in means when total
variation is computed using the new definition.

25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an