Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the time growth of the error of the DG method for advective problems   In this paper we derive a priori $L^\infty(L^2)$ and $L^2(L^2)$ error
estimates for a linear advection-reaction equation with inlet and outlet
boundary conditions. The goal is to derive error estimates for the
discontinuous Galerkin (DG) method that do not blow up exponentially with
respect to time, unlike the usual case when Gronwall's inequality is used.
While this is possible in special cases, such as divergence-free advection
fields, we take a more general approach using exponential scaling of the exact
and discrete solutions. Here we use a special scaling function, which
corresponds to time taken along individual pathlines of the flow. For advection
fields, where the time massless particles carried by the flow spend inside the
spatial domain is uniformly bounded from above by some $\widehat{T}$, we derive
$O(h^{p+1/2})$ error estimates where the constant factor depends only on
$\widehat{T}$, but not on the final time $T$. This can be interpreted as
applying Gronwall's inequality in the error analysis along individual pathlines
(Lagrangian setting), instead of physical time (Eulerian setting).

12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph