Taylor-Hood Like Finite Elements for Nearly Incompressible Strain Gradient Elasticity Problems

We propose a family of mixed finite elements that are robust for the nearly incompressible strain gradient model, which is fourth-order singular perturbed elliptic system. The element similar to [C. Taylor and P. Hood, Comput. & Fluids, 1(1973), 73–100] in Stokes flow. Using uniform discrete B-B inequality pairs, we show optimal rate convergence limit. By new regularity result both materials parameter incompressibility, prove method converges with 1/2 order solution strong boundary layer effects. Moreover, estimate numerical unperturbed second-order Numerical results smooth solutions sharp layers confirm theoretical prediction.