NUMERICAL ANALYSIS OF SOME OPTIMAL CONTROL PROBLEMS GOVERNED BY A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS

被引：14

作者：

Casas, Eduardo ^{[1
]}

Troeltzsch, Fredi ^{[2
]}

机构：

[1] Univ Cantabria, ETSI Ind & Telecomunicac, Dpto Matemat Aplicada & Ciencias Computac, E-39005 Santander, Spain

[2] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2011年 / 17卷 / 03期

关键词：

Quasilinear elliptic equations; optimal control problems; finite element approximations; convergence of discretized controls; NONMONOTONE TYPE; APPROXIMATIONS;

D O I：

10.1051/cocv/2010025

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we carry out the numerical analysis of a distributed optimal control problem governed by a quasilinear elliptic equation of non-monotone type. The goal is to prove the strong convergence of the discretization of the problem by finite elements. The main issue is to get error estimates for the discretization of the state equation. One of the difficulties in this analysis is that, in spite of the partial differential equation has a unique solution for any given control, the uniqueness of a solution for the discrete equation is an open problem.

引用

页码：771 / 800

页数：30

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