论文标题
$ hp $ -FEM用于反应扩散方程II。在角域中多长度尺度的强大指数收敛
$hp$-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains
论文作者
论文摘要
In bounded, polygonal domains $Ω\subset \mathbb{R}^2$ with Lipschitz boundary $\partialΩ$ consisting of a finite number of Jordan curves admitting analytic parametrizations, we analyze $hp$-FEM discretizations of linear, second order, singularly perturbed reaction diffusion equations on so-called geometric boundary layer meshes.我们证明，在数据上的适当分析性假设下，只要几何边界层网格可以解决问题中存在的最小长度尺度，这些$ hp $ -FEM提供了自然“能量”规范的指数收敛。数值实验证实了所提出的$ HP $ -FEM的稳健指数融合。
In bounded, polygonal domains $Ω\subset \mathbb{R}^2$ with Lipschitz boundary $\partialΩ$ consisting of a finite number of Jordan curves admitting analytic parametrizations, we analyze $hp$-FEM discretizations of linear, second order, singularly perturbed reaction diffusion equations on so-called geometric boundary layer meshes. We prove, under suitable analyticity assumptions on the data, that these $hp$-FEM afford exponential convergence in the natural "energy" norm of the problem, as long as the geometric boundary layer mesh can resolve the smallest length scale present in the problem. Numerical experiments confirm the robust exponential convergence of the proposed $hp$-FEM.
