External Approximation of Nonlinear Operator Equations

Etienne Emmrich
2009 Numerical Functional Analysis and Optimization  
Based upon an external approximation scheme for the underlying Banach space, a nonlinear operator equation is approximated by a sequence of coercive problems. The equation is supposed to be governed by the sum of two nonlinear operators acting between a reflexive Banach space and its dual. Under suitable stability assumptions and if the underlying operators can be approximated consistently, weak convergence of a subsequence of approximate solutions is shown. This also proves existence of
more » ... existence of solutions to the original equation.
doi:10.1080/01630560902987329 fatcat:fxamkck46zbo7pjirj657ofq4m