A Priori Error Estimates for Finite Element Discretizations of Parabolic Optimization Problems with Pointwise State Constraints in Time

2011 ◽  
Vol 49 (5) ◽  
pp. 1961-1997 ◽  
Author(s):  
Dominik Meidner ◽  
Rolf Rannacher ◽  
Boris Vexler
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
State Constraints ◽  
Optimization Problems ◽  
A Priori ◽  
A Priori Error Estimates ◽  
Pointwise State Constraints ◽  
Finite Element Discretizations ◽  
Priori Error Estimates ◽  
Element Discretizations

scholarly journals A priori error estimates for a linearized fracture control problem

2020 ◽  
Author(s):  
Masoumeh Mohammadi ◽  
Winnifried Wollner
Keyword(s):  
Control Problem ◽  
Error Estimates ◽  
Optimization Problems ◽  
A Priori ◽  
A Priori Error Estimates ◽  
Adjoint Variables ◽  
Conforming Finite Element Method ◽  
Priori Error Estimates ◽  
Fracture Control ◽  
Control State

Abstract A control problem for a linearized time-discrete regularized fracture propagation process is considered. The discretization of the problem is done using a conforming finite element method. In contrast to many works on discretization of PDE constrained optimization problems, the particular setting has to cope with the fact that the linearized fracture equation is not necessarily coercive. A quasi-best approximation result will be shown in the case of an invertible, though not necessarily coercive, linearized fracture equation. Based on this a priori error estimates for the control, state, and adjoint variables will be derived.

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