Solving nonlinear parabolic problems with result verification Part I: one-space dimensional case
Solving nonlinear parabolic problems with result verification Part I: one-space dimensional case
复制标题
通过结果验证解决非线性抛物线问题第一部分：一维情况
DOI：
10.1016/0377-0427(91)90179-n
复制
发表时间：
1991
影响因子：
2.4
通讯作者：
M. Nakao
中科院分区：
文献类型：
--
作者：
M. Nakao
我们提出了一些数值方法来自动证明一维抛物型初始边值问题弱解的存在性。这也意味着可以获得问题近似解的后验误差界。基于Schauder不动点定理，建立了验证条件，并利用有限元近似及其对简单抛物线问题的误差估计，提出了计算机精确解的数值验证算法。给出了经该方法验证的数值算例。
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.