Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robust Preconditioners for DG-Discretizations with Arbitrary Polynomial
  Degrees   Discontinuous Galerkin (DG) methods offer an enormous flexibility regarding
local grid refinement and variation of polynomial degrees for a variety of
different problem classes. With a focus on diffusion problems, we consider DG
discretizations for elliptic boundary value problems, in particular the
efficient solution of the linear systems of equations that arise from the
Symmetric Interior Penalty DG method. We announce a multi-stage preconditioner
which produces uniformly bounded condition numbers and aims at supporting the
full flexibility of DG methods under mild grading conditions. The constructions
and proofs are detailed in an upcoming series of papers by the authors. Our
preconditioner is based on the concept of the auxiliary space method and
techniques from spectral element methods such as Legendre-Gau{\ss}-Lobatto
grids. The presentation for the case of geometrically conforming meshes is
complemented by numerical studies that shed some light on constants arising in
four basic estimates used in the second stage.

13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex