Zeng Jinping, Chen Haowen, Xu Hongru
College of Computer Science, Dongguan University of Technology, Dongguan, Guangdong 523808 P.R. China.
College of Mathematics and Econometrics, Hunan University, Changsha, 410082 P.R. China.
J Inequal Appl. 2017;2017(1):238. doi: 10.1186/s13660-017-1513-x. Epub 2017 Sep 25.
In this paper, we consider the numerical solution for the discretization of semilinear elliptic complementarity problems. A monotone algorithm is established based on the upper and lower solutions of the problem. It is proved that iterates, generated by the algorithm, are a pair of upper and lower solution iterates and converge monotonically from above and below, respectively, to the solution of the problem. Moreover, we investigate the convergence rate for the monotone algorithm and prove quadratic convergence of the algorithm. The monotone and quadratic convergence results are also extended to the discrete problems of the two-sided obstacle problems with a semilinear elliptic operator. We also present some simple numerical experiments.
在本文中，我们考虑半线性椭圆互补问题离散化的数值解。基于该问题的上下解建立了一种单调算法。证明了由该算法生成的迭代序列是一对上下解迭代序列，并且分别从上方和下方单调收敛到该问题的解。此外，我们研究了单调算法的收敛速度并证明了该算法的二次收敛性。单调和二次收敛结果也被推广到具有半线性椭圆算子的双边障碍问题的离散问题。我们还给出了一些简单的数值实验。
