Numerical method for solving a class of nonlinear elliptic inverse problems

被引：22
作者：
Essaouini, M
Nachaoui, A
El Hajji, S
机构：
[1] Univ Mohammed 5, Fac Sci, Dept Math & Informat, Rabat, Morocco
[2] Univ Nantes, CNRS, UMR 6629, Lab Math Jean Leray, F-44322 Nantes, France
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2004年 / 162卷 / 01期
关键词：
nonlinear inverse problem; ill-posed problem; iterative method; boundary element method;
D O I：
10.1016/j.cam.2003.08.011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper discusses a method to solve a family of nonlinear inverse problems with Cauchy conditions on a part of the boundary and no condition at all on another part. An iterative boundary element procedure is proposed. The scheme uses a dynamically estimated relaxation parameter on the under-specified boundary. Various types of convergence, boundary condition formulations and effects of added small perturbations into the input data are investigated. The numerical results show that the method produces a stable reasonably approximate solution. (C) 2003 Elsevier B.V. All rights reserved.
引用
收藏
页码：165 / 181
页数：17
相关论文
共 19 条
[1]  
Badeva V., 1991, PROBLEMES INCORRECTE
[2]  
BONNET M, 1997, BOUNDARY INTEGRAL EQ
[3]  
Brebbia CA., 1984, BOUNDARY ELEMENT TEC, DOI DOI 10.1007/978-3-642-48860-3
[4]  
Grisvard P., 1985, ELLIPTIC PROBLEMS NO, V24
[5]  
HESS JL, 1990, ANNU REV FLUID MECH, V22, P255
[6]  
Jaswon M. A., 1977, Integral equation methods in potential theory and elastostatics
[7]   An alternating method for an inverse Cauchy problem [J].
Jourhmane, M ;
Nachaoui, A .
NUMERICAL ALGORITHMS, 1999, 21 (1-4) :247-260
[8]  
JOURHMANE M, IN PRESS APPL ANAL
[9]  
KOZLOV VA, 1991, COMP MATH MATH PHYS+, V31, P45
[10]  
Kurpisz K., 1995, Inverse Thermal Problems, P12
12