论文标题
在非曼菲德多面体中，具有跳跃的多项式插值
Jump-preserving polynomial interpolation in non-manifold polyhedra
论文作者
论文摘要
We construct a piecewise-polynomial interpolant $u \mapsto Πu$ for functions $u:Ω\setminus Γ\to \mathbb{R}$, where $Ω\subset \mathbb{R}^d$ is a Lipschitz polyhedron and $Γ\subset Ω$ is a possibly non-manifold $(d-1)$-dimensional高表面。这种插值在相关的sobolev规范中具有近似属性，以及一组其他代数属性，即$π^2 =π$，$π$保留了均匀的边界价值，并在$γ$上跳跃。作为一个应用程序，我们在$γ$上获得了“跳跃”运算符的有界离散右内，以及Galerkin方案的错误估算值，以在$ω$中求解二阶椭圆pde，并在$γ$上开张。
We construct a piecewise-polynomial interpolant $u \mapsto Πu$ for functions $u:Ω\setminus Γ\to \mathbb{R}$, where $Ω\subset \mathbb{R}^d$ is a Lipschitz polyhedron and $Γ\subset Ω$ is a possibly non-manifold $(d-1)$-dimensional hypersurface. This interpolant enjoys approximation properties in relevant Sobolev norms, as well as a set of additional algebraic properties, namely, $Π^2 = Π$, and $Π$ preserves homogeneous boundary values and jumps of its argument on $Γ$. As an application, we obtain a bounded discrete right-inverse of the "jump" operator across $Γ$, and an error estimate for a Galerkin scheme to solve a second-order elliptic PDE in $Ω$ with a prescribed jump across $Γ$.
