We design and analyze an iterative two-grid algorithm for the finite element discretizations of strongly nonlinear elliptic boundary value problems in this paper. We propose an iterative two-grid algorithm, in which a nonlinear problem is first solved on the coarse space, and then a symmetric positive definite problem is solved on the fine space. The innovation of this paper lies in the establishment of a first convergence analysis, which requires simultaneous estimation of four interconnected error estimates. We also present some numerical experiments to confirm the efficiency of the proposed algorithm.

翻译：本文设计并分析了一种针对强非线性椭圆边值问题有限元离散的迭代双网格算法。我们提出了一种迭代双网格方法，其中首先在粗网格空间求解非线性问题，然后在细网格空间求解对称正定问题。本文的创新之处在于建立了首个收敛性分析，这需要对四个相互关联的误差估计进行同步评估。我们还给出了一些数值实验，以验证所提算法的有效性。