scholarly journals Ciarlet–Raviart mixed finite element approximation for an optimal control problem governed by the first bi-harmonic equation

2009 ◽  
Vol 233 (2) ◽  
pp. 372-388 ◽  
Author(s):  
Weidong Cao ◽  
Danping Yang
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Mixed Finite Element ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Harmonic Equation

scholarly journals Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Zuliang Lu
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
A Posteriori Error Estimates ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Adaptive Finite Element ◽  
Element Discretization ◽  
Semilinear Parabolic

The aim of this work is to study the semidiscrete finite element discretization for a class of semilinear parabolic integrodifferential optimal control problems. We derive a posteriori error estimates inL2(J;L2(Ω))-norm andL2(J;H1(Ω))-norm for both the control and coupled state approximations. Such estimates can be used to construct reliable adaptive finite element approximation for semilinear parabolic integrodifferential optimal control problem. Furthermore, we introduce an adaptive algorithm to guide the mesh refinement. Finally, a numerical example is given to demonstrate the theoretical results.

scholarly journals Finite Element Approximation of Optimal Control Problem with Weighted Extended B-Splines

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 452 ◽  
Author(s):  
Madiha Sana ◽  
Muhammad Mustahsan
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
State Variables ◽  
B Splines ◽  
Regularity Of Solution ◽  
Distinct Aspect

In this research article, an optimal control problem (OCP) with boundary observations is approximated using finite element method (FEM) with weighted extended B-splines (WEB-splines) as basis functions. This type of OCP has a distinct aspect that the boundary observations are outward normal derivatives of state variables, which decrease the regularity of solution. A meshless FEM is proposed using WEB-splines, defined on the usual grid over the domain, R 2 . The weighted extended B-spline method (WEB method) absorbs the regularity problem as the degree of the B-splines is increased. Convergence analysis is also performed by some numerical examples.

Sign in / Sign up

Export Citation Format

Share Document