Volume locking phenomena arising in a hybrid symmetric interior penalty method with continuous numerical traces

Abstract

A hybrid version of the symmetric interior penalty (HSIP) method is considered for linear elasticity problems for nearly incompressible materials. When the 1 conforming finite element method is applied to such problems, volume locking phenomena occur. Discontinuous Galerkin (DG) methods are known as a remedy for the locking. The HSIP method has two unknowns which are approximations for the displacement and its trace on the skeleton. The latter is often called the numerical trace. The HSIP method with the discontinuous numerical trace is free from locking. On the other hand, it is numerically observed that the HSIP method with the continuous numerical trace causes volume locking phenomena when the 1 elements are employed for the two unknowns. The numerical fact is mathematically proved in this paper.