An Immersed Finite Element Method for the Elasticity Problems with Displacement Jump (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we propose a finite element method for the elasticity problemswhich have displacement discontinuity along the material interface using uniformgrids. We modify the immersed finite element method introduced recently forthe computation of interface problems having homogeneous jumps [20, 22]. Since theinterface is allowed to cut through the element, we modify the standard Crouzeix-Raviartbasis functions so that along the interface, the normal stress is continuous andthe jump of the displacement vector is proportional to the normal stress. We constructthe broken piecewise linear basis functions which are uniquely determined by theseconditions. The unknowns are only associated with the edges of element, except theintersection points. Thus our scheme has fewer degrees of freedom than most of theXFEM type of methods in the existing literature [1,8,13]. Finally, we present numericalresults which show optimal orders of convergence rates.