Convergence analysis of a weak Galerkin finite element method on a Shishkin mesh for a singularly perturbed fourth-order problem in 2D

Shicheng Liu, Xiangyun Meng, Qilong Zhai

We consider the singularly perturbed fourth-order boundary value problem ${\epsilon }^2{\Delta }^{2}u-\Delta u=f$ on the unit square $\Omega \subset {\mathbb{R}}^2$, with boundary conditions $u = \p…