Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence rates for an optimally controlled Ginzburg-Landau equation   An optimal control problem related to the probability of transition between
stable states for a thermally driven Ginzburg-Landau equation is considered.
The value function for the optimal control problem with a spatial
discretization is shown to converge quadratically to the value function for the
original problem. This is done by using that the value functions solve similar
Hamilton-Jacobi equations, the equation for the original problem being defined
on an infinite dimensional Hilbert space. Time discretization is performed
using the Symplectic Euler method. Imposing a reasonable condition this method
is shown to be convergent of order one in time, with a constant independent of
the spatial discretization.

5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
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