Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On adaptive timestepping for weakly instationary solutions of hyperbolic
  conservation laws via adjoint error control   We study a recent timestep adaptation technique for hyperbolic conservation
laws. The key tool is a space-time splitting of adjoint error representations
for target functionals due to S\"uli and Hartmann. It provides an efficient
choice of timesteps for implicit computations of weakly instationary flows. The
timestep will be very large in regions of stationary flow, and become small
when a perturbation enters the flow field. Besides using adjoint techniques
which are already well-established, we also add a new ingredient which
simplifies the computation of the dual problem. Due to Galerkin orthogonality,
the dual solution {\phi} does not enter the error representation as such.
Instead, the relevant term is the difference of the dual solution and its
projection to the finite element space, {\phi}-{\phi}h . We can show that it is
therefore sufficient to compute the spatial gradient of the dual solution, $w =
{\nabla} {\phi}$. This gradient satisfies a conservation law instead of a
transport equation, and it can therefore be computed with the same algorithm as
the forward problem, and in the same finite element space. We demonstrate the
capabilities of the approach for a weakly instationary test problem for scalar
conservation laws.

5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph