Spurious Behavior for a Numerical Scheme of Nonlinear Elliptic Equations

✍ Scribed by F. Vadillo

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 230 KB
• Volume: 121
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1995.1181

✦ Synopsis

In this paper we investigate finite difference approximations of ronlinear elliptic equations of the form (\Delta |) । (\lambda\left(\prime \prime \mid |^{\prime \prime}\right) \quad 0) in three diumensions, where (d) is a positive pratalleter. 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. ๘1995 Academic Press. Inc.