The Mortar Finite Element Method (MFEM) has been demonstrated to be a powerful technique in order to formulate a weak continuity condition at the interface of sub-domains in which different meshes, i.e. non-conforming or hybrid, and / or variational approximations are used. This is particularly suitable when coupling different physics on different domains, such as elasticity and poro-elasticity, for example, in the context of coupled flow and geomechanics. In this area precisely, geometrical aspects play also a role. It is very expensive, from the computational standpoint, having the same mesh for flow and mechanics. Tensor product meshes are usually propagated from the reservoir in a conforming way into its surroundings, which makes non-conforming discretizations a highly attractive option for these cases. In order to tackle these general sub-domains problems, a MFEM scheme on curve interfaces based on Non-Uniform Rational B-Splines (NURBS) curves and surfaces is presented in this paper. The goal is having a more robust geometrical representation for mortar spaces which allows gluing non-conforming interfaces on realistic three-dimensional geometries. The resulting mortar saddle point problem will be decoupled by means of standard Domain Decomposition techniques such as Dirichlet-Neumann and Neumann-Neumann, in order to exploit current parallel machine architectures. Three-dimensional examples ranging from near-wellbore applications to field level subsidence computations show that the proposed scheme can handle problems of practical interest. In order to facilitate the implementation of complex workflows, an advanced Python wrapper interface that allows programming capabilities have been implemented. Extensions to couple elasticity and plasticity, which seems very promising in order to speed up computations involving poroplasticity, will be also discussed.


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