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Numerical Verification of Solutions for Nonlinear Elliptic Problems Using anL∞Residual Method

✍ Scribed by Mitsuhiro T Nakao; Nobito Yamamoto

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
194 KB
Volume
217
Category
Article
ISSN
0022-247X

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✦ Synopsis

We consider a numerical enclosure method with guaranteed L ϱ error bounds for the solution of nonlinear elliptic problems of second order. By using an a posteriori error estimate for the approximate solution of the problem with a higher order C 0 -finite element, it is shown that we can obtain the guaranteed L ϱ error bounds with high accuracy. A particular emphasis is that our method needs no assumption of the existence of the solution of the original nonlinear equation, but it follows as the result of computation itself. A numerical example that confirms the effectiveness of the method is presented.

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