A posteriori error estimates for optimal distributed control governed by the evolution equations
A posteriori error estimates are used to design adaptive grids for solving partial differential equation (PDEs) by finite elements. They are used often for optimal control problems (OPC's) with PDEs, whereas most of the recent work is concentrated on elliptic equations. The authors develop a posteriori error estimates by using space-time finite elements for optimal control problems with pure parabolic problems [as in the work of \textit{D. Meidner} and \textit{B. Vexler}, SIAM J. Control Optim. 46, No.~1, 116--142 (2007; Zbl 1149.65051)], diffusion-convection problems and hyperbolic problems. It would be interesting to apply these results to design efficient adaptive space-time finite elements for OPC's with evolutionary PDE's.
scientific article; zbMATH DE number 5840215
scientific article