Optimal control under reduced regularity

被引：4

作者：

Apel, Thomas ^{[1
]}

Winkler, Gunter ^{[1
]}

机构：

[1] Univ Bundeswehr Munchen, Fak Math & Bauinformat, D-85579 Neubiberg, Germany

来源：

APPLIED NUMERICAL MATHEMATICS | 2009年 / 59卷 / 09期

关键词：

Linear quadratic optimal control problem; PDE constraints; Finite element method; Mesh grading; Postprocessing; A-priori error estimates; Superconvergence; ELLIPTIC CONTROL-PROBLEMS; BOUNDARY-VALUE-PROBLEMS; NUMERICAL APPROXIMATION; CONTROL CONSTRAINTS; MESH REFINEMENT; DISCRETIZATION; DOMAINS; EDGES;

D O I：

10.1016/j.apnum.2008.12.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with a linear quadratic optimal control problem with elliptic PDE constraints in three-dimensional domains with singularities. It is proved that the optimal control can be calculated by the finite element method at a rate of O(h(2)) provided that the mesh is sufficiently graded. The approximation of this control is computed from a piecewise constant approximation followed by a postprocessing step. Although the results are similar to the two-dimensional case, the proofs changed significantly. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：2050 / 2064

页数：15

共 31 条

[11] Error estimates for the numerical approximation of a semilinear elliptic control problem [J].

Arada, N ;

Casas, E ;

Tröltzsch, F .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2002, 23 (02) :201-229

[12] Existence of H-matrix approximants to the inverse FE-matrix of elliptic operators with L∞-coefficients [J].

Bebendorf, M ;

Hackbusch, W .

NUMERISCHE MATHEMATIK, 2003, 95 (01) :1-28

[13] Error estimates for the numerical approximation of boundary semilinear elliptic control problems [J].

Casas, E ;

Mateos, M ;

Tröltzsch, F .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2005, 31 (02) :193-219

[14]

CASAS E, 2003, ANAL OPTIMIZATION DI

[15] Using piecewise linear functions in the numerical approximation of semilinear elliptic control problems [J].

Casas, Eduardo .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 2007, 26 (1-3) :137-153

[16]

Ciarlet P.G, 2002, FINITE ELEMENT METHO, DOI DOI 10.1137/1.9780898719208

[17]

DAUGE M, 1988, LECT NOTES MATH, V1341

[18] APPROXIMATION OF A CLASS OF OPTIMAL CONTROL PROBLEMS WITH ORDER OF CONVERGENCE ESTIMATES [J].

FALK, RS .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1973, 44 (01) :28-47

[19] ASYMPTOTIC L-INFINITY-ERROR ESTIMATES FOR LINEAR FINITE-ELEMENT APPROXIMATIONS OF QUASILINEAR BOUNDARY-VALUE PROBLEMS [J].

FREHSE, J ;

RANNACHER, R .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1978, 15 (02) :418-431

[20] A variational discretization concept in control constrained optimization: The linear-quadratic case [J].

Hinze, M .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2005, 30 (01) :45-61

← 1 2 3 4 →