Numerical verifications of solutions for nonlinear elliptic equations
Numerical verifications of solutions for nonlinear elliptic equations
复制标题
非线性椭圆方程解的数值验证
DOI：
10.1007/bf03167208
复制
发表时间：
1993
影响因子：
0.9
通讯作者：
M. Nakao
中科院分区：
文献类型：
--
作者：
Yoshitaka Watanabe;M. Nakao
提出了一种数值方法，使我们能够验证非线性椭圆边值问题弱解的存在性。它是基于无限维不动点定理，使用Newton-like算子和有限元逼近的误差估计。我们还提出了一个有效的验证程序，自动生成的集合，包括在计算机中的精确解。最后给出了数值算例。
A numerical technique which enables us to verify the existence of weak solutions for nonlinear elliptic boundary value problems is proposed. It is based on the infinite dimensional fixed point theorems using the Newton-like operator and the error estimates for finite element approximations. We also present an effective verification procedure which automatically generates the set including the exact solution in a computer. Some numerical examples are illustrated.