The stability in Ws,p(Γ) spaces of L2-projections on some convex sets

被引：12

作者：

Casas, E

Raymond, JP ^{[1
]}

机构：

[1] Univ Toulouse 3, CNRS, UMR 5640, Lab MIP, F-31062 Toulouse 9, France

[2] Univ Cantabria, ETSI Ind & Telecomun, Dept Matemat Aplicada & Ciencias Computac, Santander, Spain

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2006年 / 27卷 / 02期

关键词：

numerical approximation; optimal control; projection on a convex set; stability estimates;

D O I：

10.1080/01630560600569940

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a polygonal open bounded subset of R-2, of boundary Gamma, we study stability estimates for the projection operator from L-1(Gamma) on a convex set K-h of continuous piecewise affine functions satisfying bound constraints. We establish stability estimates in L-p(Gamma) and in W-s,W-p(Gamma) for 1 <= p <= infinity and 0 < s <= 1. This kind of result plays a crucial role in error estimates for the numerical approximation of optimal control problems of partial differential equations with bilateral control constraints.

引用

页码：117 / 137

页数：21

共 6 条

[1]

Brenner S. C., 2007, Texts Appl. Math., V15

[2]

CASAS E, 2005, UNPUB ERROR ESTIMATE

[3] THE STABILITY IN LP AND W-P-1 OF THE L2-PROJECTION ONTO FINITE-ELEMENT FUNCTION-SPACES [J].