Variational discretization of parabolic control problems on evolving   surfaces with pointwise state constraints
  We consider a linear-quadratic pde constrained optimal control problem on an evolving surface with pointwise state constraints. We reformulate the optimization problem on a fixed surface and approximate the reformulated problem by a discrete control problem based on a discretization of the state equation by linear finite elements in space and a discontinuous Galerkin scheme in time. We prove error bounds for control and state. 
Michael Hinze, Heiko Kr\"oner
math.OC