An Iterative Tikhonov Regularization for Solving Singularly Perturbed Elliptic PDE

In this paper, we consider a class of singularly perturbed elliptical problems with homogeneous boundary conditions. We consider a regularized iterative method for solving such problems. Convergence analysis and error estimate are derived. The regularization parameter is chosen according to an a pri...

Full description

Saved in:
Bibliographic Details
Published in:Mediterranean journal of mathematics 2017-08, Vol.14 (4), p.1-22, Article 180
Main Authors: Rajan, M. P., Reddy, G. D.
Format: Article
Language:English
Subjects:
Boundary conditions
Elliptic differential equations
Error analysis
Finite element method
Iterative methods
Mathematics
Mathematics and Statistics
Numerical methods
Partial differential equations
Regularization
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we consider a class of singularly perturbed elliptical problems with homogeneous boundary conditions. We consider a regularized iterative method for solving such problems. Convergence analysis and error estimate are derived. The regularization parameter is chosen according to an a priori strategy. We give numerical results to illustrate that the method is implementable compared with numerical methods such as Shishkin and finite element schemes. The study demonstrates that the iterated regularized scheme can be considered as an alternate method for solving singularly perturbed elliptical problems.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-017-0980-0