Abstract
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 sub-domains, such as elasticity and poroelasticity, in the context of coupled flow and geomechanics. The MFEM is extended in this paper in order to deal with curve interfaces represented by Non-Uniform Rational B-Splines (NURBS) curves and surfaces. The goal is to have a more robust and flexible geometrical representation for mortar spaces, in order to glue non-conforming interfaces on realistic geometries, which may arise from the description of faults, horizons, etc. The resulting mortar saddle-point problem is then decoupled by means of the Dirichlet-Neumann (DN) Domain Decomposition Method (DDM).
The MFEM becomes very attractive when dealing with large problems, such as reservoir compaction and subsidence computations, as it avoids propagating tensor-product meshes emanating from the extension of the reservoir towards its surroundings, helping in this way reduce the computational cost associated to the simulations. This is validated by means of detailed comparisons between the conforming and mortar or non-conforming solutions for the same problem. Several examples of coupling that involve Continuous Galerkin FEM for mechanics coupled with slightly compressible single-phase flow demonstrate that the proposed mortar method can definitively handle problems of practical interest, including field scale computations.
