Adaptive space–time finite element methods for parabolic optimal control problems

Abstract We present, analyze, and test locally stabilized space–time finite element methods on fully unstructured simplicial meshes for the numerical solution of tracking parabolic optimal control problems with standard L 2 -regularization.We derive a priori discretization error estimates in terms local mesh-sizes shape-regular meshes. The adaptive version is driven by residual indicators, or, alternatively, indicators derived from new functional posteriori estimator. latter provides guaranteed upper bound error, but more costly than indicators. perform tests benchmark examples having different features. In particular, we consider discontinuous target form first expanding then contracting ball 3d that fixed 4d space– time cylinder.