  Accurate numerical simulation of coupled fracture/fault deformation and fluid
flow is crucial to the performance and safety assessment of many subsurface
systems. In this work, we consider the discretization and enforcement of
contact conditions at such surfaces. The bulk rock deformation is simulated
using low-order continuous finite elements, while frictional contact conditions
are imposed by means of a Lagrange multiplier method. We employ a cell-centered
finite-volume scheme to solve the fracture fluid mass balance equation. From a
modeling perspective, a convenient choice is to use a single grid for both
mechanical and flow processes, with piecewise-constant interpolation of
Lagrange multipliers, i.e., contact tractions and fluid pressure.
Unfortunately, this combination of displacement and multiplier variables is not
uniformly inf-sup stable, and therefore requires a stabilization technique.
Starting from a macroelement analysis, we develop two algebraic stabilization
approaches and compare them in terms of robustness and convergence rate. The
proposed approaches are validated against challenging analytical two- and
three-dimensional benchmarks to demonstrate accuracy and robustness. These
benchmarks include both pure contact mechanics problems and well as problems
with tightly-coupled fracture flow.
