Balanced norm estimates for rp-Finite Element Methods applied to singularly perturbed fourth order boundary value problems

09/19/2023

∙

by   Torsten Linß, et al.

∙

0

∙

share

We establish robust exponential convergence for rp-Finite Element Methods (FEMs) applied to fourth order singularly perturbed boundary value problems, in a balanced norm which is stronger than the usual energy norm associated with the problem. As a corollary, we get robust exponential convergence in the maximum norm. r p FEMs are simply p FEMs with possible repositioning of the (fixed number of) nodes. This is done for a C^1 Galerkin FEM in 1-D, and a C^0 mixed FEM in 2-D over domains with smooth boundary. In both cases we utilize the Spectral Boundary Layer mesh.