scholarly journals Adaptive variational discretization approximation method for parabolic optimal control problems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yuelong Tang ◽  
Yuchun Hua

AbstractIn this paper, we study variational discretization method for parabolic optimization problems. Firstly, we obtain some convergence and superconvergence analysis results of the approximation scheme. Secondly, we derive a posteriori error estimates of the approximation solutions. Finally, we present variational discretization approximation algorithm and adaptive variational discretization approximation algorithm for parabolic optimization problems and do some numerical experiments to confirm our theoretical results.

2021 ◽  
Vol 19 (1) ◽  
pp. 1210-1222
Author(s):  
Yuelong Tang ◽  
Yuchun Hua

Abstract In this paper, we consider an approximation scheme for fractional evolution equation with variable coefficient. The space derivative is approximated by triangular finite element and the time fractional derivative is evaluated by the L1 approximation. The main aim of this work is to provide convergence and superconvergence analysis and derive a posteriori error estimates. Some numerical examples are presented to demonstrate our theoretical results.


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