Robust exponential convergence of hp-FEM in balanced norms for singularly perturbed reaction–diffusion problems: Corner domains. (1st October 2017)

• Record Type: Journal Article
• Authors: Faustmann, M.; Melenk, J.M.
• Is Part Of: Computers & mathematics with applications. Volume 74:issue 7(2017)
• Page Start: 1576
• Page End: 1589
• Publication Date: 2017-10-01
• Subjects: High order FEM -- Singular perturbation -- Balanced norm -- Uniform estimates; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.03.015
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: The h p -version of the finite element method is applied to singularly perturbed reaction–diffusion type equations on polygonal domains. The solution exhibits boundary layers as well as corner layers. On a class of meshes that are suitably refined near the boundary and the corners, robust exponential convergence (in the polynomial degree) is shown in both a balanced norm and the maximum norm.