Conservation properties of non-conforming embedded finite-element methods based on lagrange multipliers

Numerical simulations of Darcy flow in fractured porous media rely on hybrid- or equi-dimensional fracture models. The former considers fractures as lower-dimensional manifolds, while the latter treats them as objects of the same geometrical dimension as the porous matrix. Embedded strategies remove the inherent difficulties in mesh generation for fractured media, as they employ two different non-conforming meshes. While the Continuous Galerkin discretization has been shown to be locally conservative, this property has yet to be investigated for embedded strategies. This paper demonstrates that embedded strategies, based on dual Lagrange multiplier and discretized within a Continuous Galerkin framework, are locally conservative. We conduct a numerical analysis of the conservation properties in both hybrid- and equi-dimensional models for fractured porous media. Our results strongly support the conservation properties of embedded strategies.