For the singular integral definition of the fractional Laplacian, we consider an adaptive finite element method steered by two-level error indicators. For this algorithm, we show linear convergence in two and three space dimensions as well as convergence of the algorithm with optimal algebraic rates in 2D, when newest vertex bisection is employed for mesh refinement.
翻译:对于分数拉帕西亚的单一整体定义,我们认为这是一种由两级误差指标引导的适应性有限元素方法。 对于这一算法,我们展示了两个和三个空间维度的线性趋同,以及算法与2D最佳代数率的趋同,当使用最新的脊椎分解进行网格改进时。