A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation

被引：112

作者：

Bourgeois, L ^{[1
]}

机构：

[1] Ecole Natl Super Tech Avancees, Lab POEMS, F-75739 Paris, France

来源：

INVERSE PROBLEMS | 2005年 / 21卷 / 03期

关键词：

D O I：

10.1088/0266-5611/21/3/018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work concerns the use of the method of quasi-reversibility to solve the Cauchy problem for Laplace's equation. We describe a mixed formulation of the method and its relationship with a classical formulation. A discretized formulation using finite elements of class C(0) is derived from the mixed formulation, and convergence of the solution of this discretized problem with noisy data to the exact solution is analysed. Finally, a simple numerical example is implemented in order to show the feasibility of the method.

引用

页码：1087 / 1104

页数：18

共 23 条

[1] [Anonymous], 1984, ANAL MATH CALCUL NUM
[2] BLUM J, 1989, MODERN APPL MATH
[3] Existence of approximate controls for a semilinear Laplace equation
Bodart, O
[J]. INVERSE PROBLEMS, 1996, 12 (01) : 27 - 33
[4] Bourgeois, 1998, THESIS ECOLE POLYTEC
[5] Brezis H., 1999, Analyse fonctionnelle: Theorie et applications
[6] Brezzi F., 2012, MIXED HYBRID FINITE, V15
[7] BUI HD, 1993, INTRO PROBLEMES INVE
[8] CIARLET P. G., 1978, The Finite Element Method for Elliptic Problems
[9] Solution of the Cauchy problem using iterated Tikhonov regularization
Cimetière, A
Delvare, F
Jaoua, M
Pons, F
[J]. INVERSE PROBLEMS, 2001, 17 (03) : 553 - 570
[10] COLLIFRANZONE P, 1979, 222 LAB AN NUM PAV

← 1 2 3 →