An asymptotic-preserving finite element method for a forth order singular perturbation problem with boundary layers

Abstract

We propose an asymptotic-preserving finite element method for a fourth order singular perturbation problem, which completely preserves the asymptotic transition of the underlying partial differential equation. As a representative, we analyze the NZT element and a linear convergence rate is proved for the solution with sharp boundary layer. Numerical examples in two and three dimensions are consistent with the theoretical prediction.