scholarly journals A note on a priori error estimates for augmented mixed methods

2016 ◽  
Vol 57 ◽  
pp. 139-144
Author(s):  
Tomás P. Barrios ◽  
Edwin Behrens ◽  
Rommel Bustinza
Keyword(s):  
Mixed Methods ◽  
Error Estimates ◽  
A Priori ◽  
A Priori Error Estimates ◽  
Priori Error Estimates

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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