SOLVING NONLINEAR PARABOLIC PROBLEMS WITH RESULT VERIFICATION .1. ONE-SPACE DIMENSIONAL CASE

[摘要] We propose some numerical methods for the automatic proof of existence of weak solutions for parabolic initial boundary value problems with one space dimension. It also means that one can obtain a posteriori error bounds for the approximate solutions of the problems. Based upon Schauder's fixed-point theorem, a verification condition is formulated and, by the use of finite-element approximation and its error estimates for a simple parabolic problem, we present a numerical verification algorithm of exact solutions in a computer. Some numerical examples which are verified by the method are illustrated.

[发布日期] 1991-12-23

[效力级别]  Proceedings Paper

[关键词] PARABOLIC PROBLEM;FINITE-ELEMENT METHOD;ERROR ESTIMATES;FIXED-POINT THEOREM