A numerical approach to the proof of existence of solutions for elliptic problems
A numerical approach to the proof of existence of solutions for elliptic problems
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证明椭圆问题解存在性的数值方法
DOI：
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发表时间：
1988
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通讯作者：
M. Nakao
中科院分区：
文献类型：
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作者：
M. Nakao
本文给出了用计算机证明二阶线性椭圆型边值问题弱解存在的一种方法。给出了基于Schauder不动点定理的解的存在性、唯一性和包含集验证的计算过程。利用简单泊松方程的有限元近似和误差估计的结果，迭代生成一个由函数组成的集合序列，并试图自动构造包含精确解的集合。进一步考虑了该方法的可验证性条件，并给出了验证的数值算例。
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 computing procedures to verify the existence, uniqueness and inclusion set of a solution based on Schauder’s fixed point theorem. Using the finite element approximations for some simple Poisson’s equations and the results of error estimates, we generate iteratively a set sequence composed of functions and attempt to construct automatically the set including the exact solution. Further, the conditions of verifiability by this method are considered and some numerical examples of verification are presented.