Two meshless methods for Dirichlet boundary optimal control problem governed by elliptic PDEs

Liu, Yang; Cheng, Aijie

doi:10.1016/j.camwa.2020.10.026

Cited by 8 publications

(2 citation statements)

References 19 publications

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“…A variation of this approach using conforming finite element method is discussed in [36]. Recently in [42], two meshless methods are proposed for solving the Dirichlet boundary optimal control problems governed by elliptic PDEs. The finite element analysis of Dirichlet control problems using an energy regularization is carried out in [55].…”

Section: Introductionmentioning

confidence: 99%

Mixed finite element method for a second order Dirichlet boundary control problem

Garg¹,

Porwal²

2022

Preprint

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The main aim of this article is to analyze mixed finite element method for the second order Dirichlet boundary control problem. Therein, we develop both a priori and a posteriori error analysis using the energy space based approach. We obtain optimal order a priori error estimates in the energy norm and L 2 -norm with the help of auxiliary problems. The reliability and the efficiency of proposed a posteriori error estimator is discussed using the Helmholtz decomposition. Numerical experiments are presented to confirm the theoretical findings.

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Section: Introductionmentioning

confidence: 99%

Mixed finite element method for a second order Dirichlet boundary control problem

Garg¹,

Porwal²

2022

Preprint

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“…The research on numerical methods for these problems has been an active area in recent decades. To approximate the solutions of control problems, the FEM (finite element method) proves to be a powerful method and has been used as the main method in dealing with numerical analysis for optimal control problems [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Moving Mesh Method for Solving Optimal Control Problems in Viscous Incompressible Fluid

Xue

Duan

2022

Symmetry

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An adaptive moving mesh method for optimal control problems in viscous incompressible fluid is proposed with the incompressible Navier–Stokes system used to describe the motion of the fluid. The moving distance of nodes in the adopted mesh moving strategy is found by solving a diffusion equation with source terms, and an algorithm that fully considers the characteristics of the control problem is given with symmetry reduction to the incompressible Navier–Stokes equations. Numerical examples are provided to show that the proposed algorithm can solve the optimal control problem stably and efficiently on the premise of ensuring high precision.

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Mixed finite element method for a second order Dirichlet boundary control problem

Garg

Porwal

2023

Computers & Mathematics with Applications

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Two meshless methods for Dirichlet boundary optimal control problem governed by elliptic PDEs

Cited by 8 publications

References 19 publications

Mixed finite element method for a second order Dirichlet boundary control problem

Mixed finite element method for a second order Dirichlet boundary control problem

An Adaptive Moving Mesh Method for Solving Optimal Control Problems in Viscous Incompressible Fluid

Mixed finite element method for a second order Dirichlet boundary control problem

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