Analytical and computational assessment of locking in the hp finite element method Original Research Article

Locking is the phenomenon by which the numerical approximation of parameter-dependent problems deteriorates for values of the parameter close to a limiting value. In this paper, we give a definition of locking and develop precise computable and analytic ways to quantify it. Using the example of nearly incompressible elasticity, we show by means of computational and theoretical results, the difference between the h version and php version in combatting locking. Our results establish the superiority of high-order elements (both h, p and hp) when the standard variational form is used. We also discuss other issues such as curved elements, mixed methods, and locking phenomena for problems over anisotropic materials and over thin domains.