Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Space-time adaptive ADER discontinuous Galerkin finite element schemes
  with a posteriori sub-cell finite volume limiting   In this paper we present a novel arbitrary high order accurate discontinuous
Galerkin (DG) finite element method on space-time adaptive Cartesian meshes
(AMR) for hyperbolic conservation laws in multiple space dimensions, using a
high order \aposteriori sub-cell ADER-WENO finite volume \emph{limiter}.
Notoriously, the original DG method produces strong oscillations in the
presence of discontinuous solutions and several types of limiters have been
introduced over the years to cope with this problem. Following the innovative
idea recently proposed in \cite{Dumbser2014}, the discrete solution within the
troubled cells is \textit{recomputed} by scattering the DG polynomial at the
previous time step onto a suitable number of sub-cells along each direction.
Relying on the robustness of classical finite volume WENO schemes, the sub-cell
averages are recomputed and then gathered back into the DG polynomials over the
main grid. In this paper this approach is implemented for the first time within
a space-time adaptive AMR framework in two and three space dimensions, after
assuring the proper averaging and projection between sub-cells that belong to
different levels of refinement. The combination of the sub-cell resolution with
the advantages of AMR allows for an unprecedented ability in resolving even the
finest details in the dynamics of the fluid. The spectacular resolution
properties of the new scheme have been shown through a wide number of test
cases performed in two and in three space dimensions, both for the Euler
equations of compressible gas dynamics and for the magnetohydrodynamics (MHD)
equations.

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The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph