An application of the Kantorovich theorem to nonlinear finite element analysis
The author proves the existence as well as a priori error estimates for a finite element solution to a nonlinear problem by means of the Kantorovich theorem. This theorem is more known in the context of the numerical solution using Newton's iteration. The problem under consideration covers elliptic boundary value problems in 1, 2, or 3 dimensions with a strong nonlinearity: Find \(u= u(x)\) such that \[ \text{div }a(x,u, \text{grad }u)= f(x,u, \text{grad }u). \]
scientific article; zbMATH DE number 1398750