On volumetric locking in a hybrid symmetric interior penalty method for nearly incompressible linear elasticity on polygonal meshes

Abstract

A hybrid version of a symmetric interior penalty method for nearly incompressible linear elasticity is investigated. When a lifting term is used in the method, the method can be free of volumetric locking. On the other hand, when the lifting term is not used, an interior penalty parameter has to be taken to be of order $$\lambda $$ , the first Lame parameter, as $$\lambda $$ tends to infinity, in order to guarantee the coercivity of the bilinear form in the method. Taking the interior penalty parameter to be of order $$\lambda $$ leads to volumetric locking phenomena when piecewise linear functions are employed to compute approximate solutions.