  In this paper we develop a simple finite element method for simulation of
embedded layers of high permeability in a matrix of lower permeability using a
basic model of Darcy flow in embedded cracks. The cracks are allowed to cut
through the mesh in arbitrary fashion and we take the flow in the crack into
account by superposition. The fact that we use continuous elements leads to
suboptimal convergence due to the loss of regularity across the crack. We
therefore refine the mesh in the vicinity of the crack in order to recover
optimal order convergence in terms of the global mesh parameter. The proper
degree of refinement is determined based on an a priori error estimate and can
thus be performed before the actual finite element computation is started.
Numerical examples showing this effect and confirming the theoretical results
are provided. The approach is easy to implement and beneficial for rapid
assessment of the effect of crack orientation and may for example be used in an
optimization loop.
