A Numerical Method to Verify the Invertibility of Linear Elliptic Operators with Applications to Nonlinear Problems
A Numerical Method to Verify the Invertibility of Linear Elliptic Operators with Applications to Nonlinear Problems
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DOI：
10.1007/s00607-004-0111-1
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发表时间：
2005-07
期刊：
影响因子：
3.7
通讯作者：
M. Nakao;K. Hashimoto;Yoshitaka Watanabe
中科院分区：
文献类型：
--
作者：
M. Nakao;K. Hashimoto;Yoshitaka Watanabe
本文提出了一种数值方法来验证二阶线性椭圆算子的可逆性。通过使用投影和构造性的优先误差估计，可逆性条件被制定为一个数值不等式的基础上，现有的验证方法最初开发的作者之一。作为结果的一个有用的应用，我们提出了一种新的非线性椭圆问题解的验证方法，使我们能够简化验证过程。几个数值例子证实了该方法的实际有效性。
In this paper, we propose a numerical method to verify the invertibility of second-order linear elliptic operators. By using the projection and the constructivea priorierror estimates, the invertibility condition is formulated as a numerical inequality based upon the existing verification method originally developed by one of the authors. As a useful application of the result, we present a new verification method of solutions for nonlinear elliptic problems, which enables us to simplify the verification process. Several numerical examples that confirm the actual effectiveness of the method are presented.