Balanced norm estimates for -Finite Element Methods applied to singularly perturbed fourth order boundary value problems
arXiv:2309.10387
Abstract
We establish robust exponential convergence for -Finite Element Methods (FEMs) applied to fourth order singularly perturbed boundary value problems, in a \emph{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. FEMs are simply FEMs with possible repositioning of the (fixed number of) nodes. This is done for a Galerkin FEM in 1-D, and a mixed FEM in 2-D over domains with smooth boundary. In both cases we utilize the \emph{Spectral Boundary Layer} mesh.
17 pages