Mesh independence principle for nonlinear equations on hilbert spaces by preconditioning

Abstract

In the paper [2] the author prove that, under certain assumptions, the Mesh Independence Principle is satisfied for a class of nonlinear operator equations (on Banach spaces) and their discretizations. In this paper we show that, under few natural assumptions, the same results can be obtained for a class of nonlinear operator equations on Hilbert spaces and a family of preconditioned finite element discretizations of them. We also obtain (using a different proof technique) a generalization of some similar results from the paper [1]. In the last section of the paper we present numerical examples which confirm our theoretical results from the previous ones.

Keywords:

• Nonlinear operator equations
• Newton's method
• mesh independence principle
• preconditioning

AMS (MOS) Subject Classijication:

• 65S15
• 65B05
• 65L50
• 65M50

C.R. Categories:

• G.1.3