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：我们设计并分析了本文中强烈的非线性椭圆边界值问题的有限元素分解的迭代双格算法。我们提议了一种迭代双格算法,其中非线性问题首先在粗糙的空间上解决,然后在精细的空间上解决一个对称正确定的问题。本文的革新在于建立第一次趋同分析,这需要同时估计四个相互关联的误差估计数。我们还提出了一些数字实验,以确认提议的算法的效率。
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