论文标题
负顺序Sobolev空间的多级分解和规范
Multilevel decompositions and norms for negative order Sobolev spaces
论文作者
论文摘要
我们考虑在$ h^{ - s} $中稳定的$ s \ in（0,1）$中的稳定的分段常数的多级分解。在统一和局部精制的网格的情况下给出了证明。我们的发现可以应用于定义局部多级对角线预处理，该预处理导致条件数（与网格尺寸和水平无关）并具有最佳的计算复杂性。此外，我们讨论了基于局部（Quasi）投影运算符的多级规范，这些规范允许对负顺序Sobolev规范进行有效评估。数值示例和关于几个扩展和应用的讨论总结了本文。
We consider multilevel decompositions of piecewise constants on simplicial meshes that are stable in $H^{-s}$ for $s\in (0,1)$. Proofs are given in the case of uniformly and locally refined meshes. Our findings can be applied to define local multilevel diagonal preconditioners that lead to bounded condition numbers (independent of the mesh-sizes and levels) and have optimal computational complexity. Furthermore, we discuss multilevel norms based on local (quasi-)projection operators that allow the efficient evaluation of negative order Sobolev norms. Numerical examples and a discussion on several extensions and applications conclude this article.
