scholarly journals SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 723
Author(s):  
Qiming Wang ◽  
Zhaojie Zhou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Diffusion Equation ◽  
Control Problem ◽  
State Equation ◽  
The State ◽  
Virtual Element Method ◽  
Adjoint State ◽  
Virtual Element ◽  
Convection Dominated

In this paper, the streamline upwind/Petrov Galerkin (SUPG) stabilized virtual element method (VEM) for optimal control problem governed by a convection dominated diffusion equation is investigated. The virtual element discrete scheme is constructed based on the first-optimize-then-discretize strategy and SUPG stabilized virtual element approximation of the state equation and adjoint state equation. An a priori error estimate is derived for both the state, adjoint state, and the control. Numerical experiments are carried out to illustrate the theoretical findings.

scholarly journals Ana posteriorierror analysis for an optimal control problem with point sources

2018 ◽  
Vol 52 (5) ◽  
pp. 1617-1650 ◽  
Author(s):  
Alejandro Allendes ◽  
Enrique Otárola ◽  
Richard Rankin ◽  
Abner J. Salgado
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Weighted Sobolev Spaces ◽  
Control Variable ◽  
The State ◽  
Point Sources ◽  
Adjoint Equations ◽  
Error Estimator ◽  
A Posteriori

We propose and analyze a reliable and efficienta posteriorierror estimator for a control-constrained linear-quadratic optimal control problem involving Dirac measures; the control variable corresponds to the amplitude of forces modeled as point sources. The proposeda posteriorierror estimator is defined as the sum of two contributions, which are associated with the state and adjoint equations. The estimator associated with the state equation is based on Muckenhoupt weighted Sobolev spaces, while the one associated with the adjoint is in the maximum norm and allows for unbounded right hand sides. The analysis is valid for two and three-dimensional domains. On the basis of the deviseda posteriorierror estimator, we design a simple adaptive strategy that yields optimal rates of convergence for the numerical examples that we perform.

scholarly journals Spectral Galerkin Approximation of Space Fractional Optimal Control Problem with Integral State Constraint

2021 ◽  
Vol 5 (3) ◽  
pp. 102
Author(s):  
Fangyuan Wang ◽  
Xiaodi Li ◽  
Zhaojie Zhou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Jacobi Polynomials ◽  
A Priori ◽  
Galerkin Approximation ◽  
State Constraint ◽  
Diffusion Reaction ◽  
Lagrangian Multiplier ◽  
Adjoint State

In this paper spectral Galerkin approximation of optimal control problem governed by fractional advection diffusion reaction equation with integral state constraint is investigated. First order optimal condition of the control problem is discussed. Weighted Jacobi polynomials are used to approximate the state and adjoint state. A priori error estimates for control, state, adjoint state and Lagrangian multiplier are derived. Numerical experiment is carried out to illustrate the theoretical findings.

scholarly journals Optimal Control of Plasticity with Inertia

2021 ◽  
Vol Volume 2 (Original research articles) ◽  
Author(s):  
Stephan Walther
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Monotone Operator ◽  
Maximal Monotone Operator ◽  
Kinematic Hardening ◽  
Maximal Monotone ◽  
Small Strain ◽  
State Equation ◽  
Elasto Plasticity

The paper is concerned with an optimal control problem governed by the equations of elasto plasticity with linear kinematic hardening and the inertia term at small strain. The objective is to optimize the displacement field and plastic strain by controlling volume forces. The idea given in [10] is used to transform the state equation into an evolution variational inequality (EVI) involving a certain maximal monotone operator. Results from [27] are then used to analyze the EVI. A regularization is obtained via the Yosida approximation of the maximal monotone operator, this approximation is smoothed further to derive optimality conditions for the smoothed optimal control problem.

Sign in / Sign up

Export Citation Format

Share Document