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Corpus ID: 55794893

Numerical Verification Methods for the Solutions of Nonlinear Elliptic and Evolution Problems

@inproceedings{Nakao1992NumericalVM,
title={Numerical Verification Methods for the Solutions of Nonlinear Elliptic and Evolution Problems},
author={Mitsuhiro T. Nakao},
year={1992}
}

In this paper, we consider a numerical technique to enclose the solutions with guaranteed error bounds for nonlinear elliptic bundary value problems as well as its extension to the evolution equations. Using a finite element solution and explicit error estimate for certain simple hnear problem, we construct, in computer, a set of functions which satisfies the condition of Schauder’s or other fixed point theorem under some appropriately function spaces. In order to obtain such a numerical set… Expand

In this paper, we describe a method which proves by computers the existence of weak solutions for linear elliptic boundary value problems of second order. It is shown that we can constitute the… Expand

We analyze the Galerkin approximation of the general second-order parabolic initial-boundary value problem. For the second-order continuous time method with initial data only in $L^2 $ we prove an… Expand