Abstract
The mesh-independence principle asserts that, when Newton’s method is applied to a nonlinear equation between some Banach spaces as well as to some finite-dimensional discretization of that equation, then the behavior of the discretized process is asymptotically the same as that for the original iteration and, as a consequence, the number of steps required by the two processes to converge to within a given tolerance is essentially the same. So far this result has been proved only for certain classes of boundary value problems. In this paper a proof is presented for a general class of operator equations and discretizations. It covers the earlier results and extends them well beyond the cases that have been considered before.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
