Mixed and Nitsche’s discretizations of Coulomb frictional contact-mechanics for mixed dimensional poromechanical models

This work deals with the discretization of single-phase Darcy flows in fractured and deformable porous media, including frictional contact at matrix–fracture interfaces. Fractures are described as a network planar surfaces leading to so-called mixed-dimensional models. Small displacements linear poro-elastic behavior considered matrix. One key difficulty simulate such coupled poro-mechanical models is related formulation mechanical sub-problem. Our starting point based on mixed using facewise constant Lagrange multipliers along fractures representing normal tangential stresses. natural choice for dual cone order account complex fracture networks corners intersections. It leads local expressions conditions efficient semi-smooth nonlinear solvers. On other hand, requires satisfy compatibility condition between discrete spaces restricting displacement space potentially sub-optimal accuracy. motivates investigation two alternative formulations either stabilized or Nitsche’s method. These three types first investigated theoretically enhance their connections. Then, they compared numerically terms accuracy convergence. The sensitivity parameters also investigated. Several 2D test cases various both P1 P2 conforming Finite Element discretizations field an Hybrid Volume flow model.