论文标题
$ h^1 $ - $ l^2 $ - 预测到适应性精制的四边形网格上的有限元空间
$H^1$-Stability of the $L^2$-Projection onto Finite Element Spaces on Adaptively Refined Quadrilateral Meshes
论文作者
论文摘要
$ l^2 $ - 正交投影$π_h：l^2（ω）\ rightArrow \ Mathbb {v} _H $上的有限元（Fe）$ \ Mathbb {V} _H $称为$ h^1 $ h^1 $ - 稳定iff $ h^1 $ - stable iff $ \ \nablaπ_h| c \ | u \ | _ {h^1（ω）} $，对于任何$ u \ in H^1（ω）$，带有正常数$ c \ neq c（h）$独立于网格尺寸$ h> 0 $。在这项工作中，我们讨论了适应性精制网格的$ h^1 $稳定性的本地标准。我们表明，最初在Bank等人中引入的2D（Q-RG和Q-RB）中四边形网格的自适应精炼策略。 1982年和Kobbelt 1996，是$ h^1 $ - 稳定的多项式$ p = 2，\ ldots，9 $。
The $L^2$-orthogonal projection $Π_h:L^2(Ω)\rightarrow\mathbb{V}_h$ onto a finite element (FE) space $\mathbb{V}_h$ is called $H^1$-stable iff $\|\nablaΠ_h u\|_{L^2(Ω)}\leq C\|u\|_{H^1(Ω)}$, for any $u\in H^1(Ω)$ with a positive constant $C\neq C(h)$ independent of the mesh size $h>0$. In this work, we discuss local criteria for the $H^1$-stability of adaptively refined meshes. We show that adaptive refinement strategies for quadrilateral meshes in 2D (Q-RG and Q-RB), introduced originally in Bank et al. 1982 and Kobbelt 1996, are $H^1$-stable for FE spaces of polynomial degree $p=2,\ldots,9$.
