Lardy's regularization of a singularly perturbed elliptic PDE

Authors:
Arindama Singh;S. Sheela
Affiliations:
Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India;Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

Citing 2
Cited 0

Tikhonov regularization of an elliptic PDE

Mathematics and Computers in Simulation
Corrigendum: Corrigendum to "Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems I: Reaction-diffusion type" [Comput. Math. Appl. 35 (3) (1998) 57-70]

Computers & Mathematics with Applications

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Abstract

In this paper, we consider an elliptic partial differential equation where a small parameter is multiplied with one or both of the second derivatives. Viewing it as an ill-posed problem, Lardy's regularization method is applied to approximate the solution. Convergence of the regularized solution to the original is proved. Numerical examples have been included for illustrating the method.