论文标题
适应性迭代线性化有限元方法的能量收缩和最佳收敛性
Energy contraction and optimal convergence of adaptive iterative linearized finite element methods
论文作者
论文摘要
我们重新审视了希尔伯特空间中非线性方程的迭代解的统一方法。我们的主要观察结果是[Heid＆Wihler，数学。 comp。 89（2020），Calcolo 57（2020）]在（摘要）强烈单调问题的背景下满足了能量收缩特性。反过来，该特性是[Gantner等人，Arxiv：2003.10785]的最新收敛分析中的关键要素。特别是，我们推断出适应性迭代线性化有限元方法（AILFEMS）导致完全线性收敛，并且相对于自由度以及总计算时间，最佳代数速率具有最佳的代数速率。
We revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert spaces. Our key observation is that the general approach from [Heid & Wihler, Math. Comp. 89 (2020), Calcolo 57 (2020)] satisfies an energy contraction property in the context of (abstract) strongly monotone problems. This property, in turn, is the crucial ingredient in the recent convergence analysis in [Gantner et al., arXiv:2003.10785]. In particular, we deduce that adaptive iterative linearized finite element methods (AILFEMs) lead to full linear convergence with optimal algebraic rates with respect to the degrees of freedom as well as the total computational time.
