A PRIORI ERROR ESTIMATES FOR A FINITE ELEMENT DISCRETIZATION OF PARABOLIC OPTIMIZATION PROBLEMS WITH POINTWISE CONSTRAINTS IN TIME ON MEAN VALUES OF THE GRADIENT OF THE STATE

作者：Ludovici Francesco^*; Wollner Winnifried

来源：SIAM Journal on Control and Optimization, 2015, 53(2): 745-770.

DOI：10.1137/140961778

• parabolic optimization
• gradient state constraints
• pointwise in time constraints
• space-time a priori error

This article is concerned with the discretization of parabolic optimization problems subject to pointwise in time constraints on mean values of the derivative of the state variable. Central components of the analysis are a priori error estimates for the dG(0)-cG(1) discretization of the parabolic partial differential equation (PDE) in the L-infinity(0,T;H-0(1)(Omega))-norm, together with corresponding estimates in L-1(0,T;H-0(1)(Omega)) for the adjoint PDE. These results are then utilized to show convergence orders for the discrete approximation toward the solution of the parabolic optimization problem.

• 出版日期2015