Solving Nonlinear Elliptic Problems with Result Verification Using an H -1 Type Residual Iteration
Solving Nonlinear Elliptic Problems with Result Verification Using an H -1 Type Residual Iteration
复制标题
使用 H -1 型残差迭代解决非线性椭圆问题并验证结果
DOI：
10.1007/978-3-7091-6918-6_13
复制
发表时间：
1993
影响因子：
1.3
通讯作者：
M. Nakao
中科院分区：
文献类型：
--
作者：
M. Nakao
用H-1型剩余迭代法求解非线性椭圆问题及其结果验证本文考虑一种数值方法来验证非线性椭圆边值问题的解的保误差界。利用Poisson方程的C°有限元解和显式误差估计，在计算机上构造了一组满足Sobolev空间上凝聚映射的Sadovskii不动点定理假设的函数.特别地，我们提出了一种H-1型残差迭代方法，提高了验证能力。一个数值例子，证实了该方法的有效性。
Solving Nonlinear Elliptic Problems with Result Verification Using an H -1 Type Residual Iteration. In this paper, we consider a numerical technique to verify the solutions with guaranteed error bounds for nonlinear elliptic boundary value problems. Using the C° finite element solution and explicit error estimates for the Poisson equation, we construct, in a computer, a set of functions which satisfies the hypothesis of Sadovskii’s fixed point theorem for confdensing map on a certain Sobolev space. Particularly, we propose an H -1 type residual iteration method which improves the ability of verification. A numerical example which confirms the usefulness of the method is presented.