In this paper,the finite element approximation of a class of semilinear parabolic optimal control problems with pointwise control constraint is studied.We discretize the state and co-state variables by piecewise linear continuous functions,and the control variable is approximated by piecewise constant functions or piecewise linear discontinuous functions.Some a priori error estimates are derived for both the control and state approximations.The convergence orders are also obtained.
Asymptotic error expansions in H^1-norm for the bilinear finite element approximation to a class of optimal control problems are derived for rectangular meshes. With the rectan- gular meshes, the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied. The higher order numerical approximations are used to generate a posteriori error estimators for the finite element approximation.
In this paper, we deal with a class of one-dimensional backward doubly stochastic differential equations （BDSDEs）. We obtain a generalized comparison theorem and a generalized existence theorem of BDSDEs.
