论文标题
INF-SUP稳定性意味着准正交性
Inf-sup stability implies quasi-orthogonality
论文作者
论文摘要
我们通过提出对基础问题的INF-SUP稳定性直接遵循的非对称性，无限和时间依赖性问题的自适应网状细化算法证明了新的最佳结果。这完全消除了自适应网状精炼算法的最佳融合的现代证明的中心技术困难，并导致简单的最佳证明是taylor-hood satotary Stokes问题的离散化，这是一种有限的元素/边界元素元素元素的离散，对不含水的传输问题和适应性时间固定方程的均等方程进行了分配。主要的技术工具是用于矩阵的LU因素化的新稳定性界限，以及最近建立的准正交性和基质分解之间的联系。
We prove new optimality results for adaptive mesh refinement algorithms for non-symmetric, indefinite, and time-dependent problems by proposing a generalization of quasi-orthogonality which follows directly from the inf-sup stability of the underlying problem. This completely removes a central technical difficulty in modern proofs of optimal convergence of adaptive mesh refinement algorithms and leads to simple optimality proofs for the Taylor-Hood discretization of the stationary Stokes problem, a finite-element/boundary-element discretization of an unbounded transmission problem, and an adaptive time-stepping scheme for parabolic equations. The main technical tool are new stability bounds for the LU-factorization of matrices together with a recently established connection between quasi-orthogonality and matrix factorization.
