论文标题
自适应保证较低的特征值和最佳收敛速率
Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates
论文作者
论文摘要
可以使用最近推出的最近引入的超稳定性的不合格的Crouzeix-Raviart（$ M = 1 $）或Morley（$ M = 2 $）有限元元素EIGENSOLVER，可以为$ M $ th Laplace操作员计算保证的下迪里奇特征值（GLB）。关于新自适应本素的优越性的数值证据在本文中激发了收敛分析，并证明了GLB最佳收敛速率朝着简单的特征值。该证明基于（概括）已知的抽象参数，名为“适应性公理”。除了已知的先验收敛速率外，本文中还包含了MEDIUS分析，以证明结果最佳。此和从属的$ l^2 $的本地精制三角剖分估计似乎具有独立的兴趣。自适应网状算法的最佳收敛速率的分析以$ 3 $ d进行，并突出显示了新版本的离散可靠性。
Guaranteed lower Dirichlet eigenvalue bounds (GLB) can be computed for the $m$-th Laplace operator with a recently introduced extra-stabilized nonconforming Crouzeix-Raviart ($m=1$) or Morley ($m=2$) finite element eigensolver. Striking numerical evidence for the superiority of a new adaptive eigensolver motivates the convergence analysis in this paper with a proof of optimal convergence rates of the GLB towards a simple eigenvalue. The proof is based on (a generalization of) known abstract arguments entitled as the axioms of adaptivity. Beyond the known a priori convergence rates, a medius analysis is enfolded in this paper for the proof of best-approximation results. This and subordinated $L^2$ error estimates for locally refined triangulations appear of independent interest. The analysis of optimal convergence rates of an adaptive mesh-refining algorithm is performed in $3$D and highlights a new version of discrete reliability.
