Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Crank-Nicolson time stepping and variational discretization of
  control-constrained parabolic optimal control problems   We consider a control constrained parabolic optimal control problem and use
variational discretization for its time semi-discretization. The state equation
is treated with a Petrov-Galerkin scheme using a piecewise constant Ansatz for
the state and piecewise linear, continuous test functions. This results in
variants of the Crank-Nicolson scheme for the state and the adjoint state.
Exploiting a superconvergence result we prove second order convergence in time
of the error in the controls. Moreover, the piecewise linear and continuous
parabolic projection of the discrete state on the dual time grid provides a
second order convergent approximation of the optimal state without further
numerical effort. Numerical experiments confirm our analytical findings.

11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
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