Mixed methods for interface problems

Abstract

Interface problems, where the displacement field presents a discontinuity across a surface that is related to the (continuous) normal component of the stress, arise in structural mechanic applications, such as bonded structure or fracture problems. In the numerical modeling, obtaining a highly accurate approximation of the stress near the interface might be of great importance. In these situations, it is advantageous to base numerical approximations on mixed formulations of the problems, where both the displacement and the stress appear as distinct variables—rather than on purely displacement formulations. This chapter discusses a simplified model problem that is at the basis of several realistic situations. It presents discontinuous Galerkin discretizations of interface problems in mixed formulation arising in structural mechanic applications. The interface condition links the jump of the displacement field and the normal component of the stress field.