The linearization method for the numerical analysis of finite element solutions to quasi-linear elliptic partial differential equations

摘要

Linearization methods have been used in the numerical analysis of finite element solutions to nonlinear partial differential equations (PDEs) for quite a long time. Frequently, essential properties such as differentiability of the nonlinear operator and boundedness and invertibility properties for linearized operators are assumed without deeper considerations. In this work we describe the main difficulties and build a framework which is able to circumvent them, allowing for the consideration of larger classes of problems. A priori error estimates are developed using that framework and a model problem is presented which illustrates the main results of this paper. [References: 22]