Uniformly Convergent Nonconforming Element for 3-D Fourth Order Elliptic Singular Perturbation Problem

Abstract

In this paper, using a bubble function, we construct a cuboid element to solve the fourth order elliptic singular perturbation problem in three dimensions. We prove that the nonconforming $C^0$-cuboid element converges in the energy norm uniformly with respect to the perturbation parameter.