2020/04/22 by Lehel Banjai, Jens M. Melenk, Christoph Schwab · 1 voice
Mathematics · #math.NA
paper · pdf · doi:10.1093/imanum/drac070}
arxiv published 2020/04/22 · arxiv updated 2020/09/28
In bounded, polygonal domains Ω⊂ ℝ2 with Lipschitz boundary ∂Ω 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.