Spurious Behavior for a Numerical Scheme of Nonlinear Elliptic Equations

Author: Vadillo F.

Source: Journal of Computational Physics, Volume 121, Number 1, October 1995 , pp. 94-101(0)

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Abstract:

In this paper we investigate finite difference approximations of nonlinear elliptic equations of the form Delta u | lambda (u | u^p) 0 in three dimensions, where lambda is a positive parameter. We show the existence of spurious solution branches, these solutions are spurious in the sense that they are not solutions of the differential problem. We also construct a modified problem describing the behaviour of numerical solutions, so the finite difference method may be regarded as an approximation of the modified problem. We present the results of some numerical experiments to substantiate our claims.Copyright 1995, 1999 Academic Press

Language: English

Document Type: Research article

Affiliations: Departmento de Matematica Aplicada y Estadística e I. O., Facultad de Ciencias, Universidad del Pais Vasco, Apartado 644, 48080 Bilbao, Spain

Publication date: 1995-10-01