A Morley–Wang–Xu Element Method for a Fourth Order Elliptic Singular Perturbation Problem

A Morley–Wang–Xu (MWX) element method with a simply modified right hand side is proposed for fourth order elliptic singular perturbation problem, in which the discrete bilinear form standard as usual nonconforming finite methods. The sharp error analysis given this MWX method. And Nitsche’s technique applied to MXW achieve optimal convergence rate case of boundary layers. An important feature solver-friendly. Based on Stokes complex two dimensions, decoupled into one Lagrange Poisson equation, Morley methods equation and $$P_1$$ – $$P_0$$ Brinkman implies efficient robust solvers Some numerical examples are provided verify theoretical results.