论文标题
HP FEM的指数收敛于多边形的积分分数laplacian
Exponential Convergence of hp FEM for the Integral Fractional Laplacian in Polygons
论文作者
论文摘要
我们证明，对于$ HP $ $ hp $有限元离散的能源规范的指数收敛，用于订单$ 2S \ in（0,2）$的订单$ 2S \ in（0,2）$的均匀dirichlet dirichlet边界条件的均值融合。分析中的关键成分是我们以前的工作的加权分析规律性，以及针对$ \partialΩ$的各向异性几何细节的网格。
We prove exponential convergence in the energy norm of $hp$ finite element discretizations for the integral fractional diffusion operator of order $2s\in (0,2)$ subject to homogeneous Dirichlet boundary conditions in bounded polygonal domains $Ω\subset \mathbb{R}^2$. Key ingredient in the analysis are the weighted analytic regularity from our previous work and meshes that feature anisotropic geometric refinement towards $\partialΩ$.
