A mesh independence principle for nonlinear equations using newton's method ano nonlinear projections.
Argyros, Ioannis K.
We consider the nonlinear operator equation in a Banach space. We make use of nonlinear projections on finite dimensional spaces to produce the finite dimensional discretization of the nonlinear equation. Using Newton's method we then prove the mesh-independence principle for this problem. Our results cover and extend previous results involving linear projections on finite dimensional spaces.