𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A direct approach to the finite element solution of elliptic optimal control problems

✍ Scribed by Dan Givoli

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
384 KB
Volume
15
Category
Article
ISSN
0749-159X

No coin nor oath required. For personal study only.

✦ Synopsis

A general framework is developed for the finite element solution of optimal control problems governed by elliptic nonlinear partial differential equations. Typical applications are steady-state problems in nonlinear continuum mechanics, where a certain property of the solution (a function of displacements, temperatures, etc.) is to be minimized by applying control loads. In contrast to existing formulations, which are based on the ''adjoint state,'' the present formulation is a direct one, which does not use adjoint variables. The formulation is presented first in a general nonlinear setting, then specialized to a case leading to a sequence of quadratic programming problems, and then specialized further to the unconstrained case. Linear governing partial differential equations are also considered as a special case in each of these categories.

πŸ“œ SIMILAR VOLUMES

A control volume finite element numerica
A control volume finite element numerical solution of creep problems
✍ W. J. Ferguson πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 191 KB πŸ‘ 2 views

This paper presents the novel application of a vertex-centred control volume numerical scheme commonly known as the control volume finite element method to creep problems. The discretization procedure is described in detail and is valid for both structured and unstructured grids without alteration t

FINITE ELEMENT SOLUTION OF A MODEL FREE
FINITE ELEMENT SOLUTION OF A MODEL FREE SURFACE PROBLEM BY THE OPTIMAL SHAPE DESIGN APPROACH
✍ GEORGE MEJAK πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 277 KB πŸ‘ 1 views

Optimal shape design approach is applied to numerical computation of a model potential free boundary value problem. The problem is discretized using the ΓΏnite element method. To test the approach the problem is formulated in both velocity potential and stream function formulation and four di erent ΓΏ

A numerical solution to the matrix β„‹2/β„‹βˆž
A numerical solution to the matrix β„‹2/β„‹βˆž optimal control problem
✍ G. D. Halikias; I. M. Jaimoukha; D. A. Wilson πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 158 KB πŸ‘ 1 views

In this paper a numerical solution is obtained to the problem of minimizing an H -type cost subject to an H -norm constraint. The method employed is based on the convex alternating projection algorithm and generalizes a recent technique to the multivariable case. The solution is derived in terms of