Superconvergence analysis of fully discrete finite element methods for semilinear parabolic optimal control problems

2013 ◽  
Vol 8 (2) ◽  
pp. 443-464 ◽  
Author(s):  
Yuelong Tang ◽  
Yanping Chen
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Finite Element Methods ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Fully Discrete ◽  
Discrete Finite Element ◽  
Parabolic Optimal Control ◽  
Semilinear Parabolic

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

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ulrich Langer ◽  
Andreas Schafelner
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Finite Element Methods ◽  
Optimal Control Problems ◽  
Space Time ◽  
Residual Error ◽  
Control Problems ◽  
Error Estimator ◽  
Parabolic Optimal Control ◽  
Error Indicators

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

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