A Posteriori Existence in Numerical Computations
نویسنده
چکیده
It is shown that, if the residual of a stable numerical solution is sufficiently small, there exists a nearby exact solution for which an a posteriori error estimate holds. This result demonstrates that it is not necessary to assume the existence of exact solutions in a posteriori error analysis for nonlinear equations. The concept is analyzed in an abstract Banach space setting and its practicality shown at two numerical examples. Possible applications include an improved a posteriori error analysis for nonlinear equations but also a numerical investigation of the existence of solutions to nonlinear (partial differential) equations where insufficient analytical knowledge is available.
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عنوان ژورنال:
- SIAM J. Numerical Analysis
دوره 47 شماره
صفحات -
تاریخ انتشار 2009