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Geological settings with reservoir characteristics include fractures withdifferent material and geometrical properties. Hence, numerical simulations inapplied geophysics demands for computational frameworks which efficiently allowto integrate various fracture geometries in a porous medium matrix. This studypresents a modeling approach for single-phase flow in fractured porous mediaand its application to different types of non-conforming mesh models. Wepropose a combination of the Lagrange multiplier method with variationaltransfer to allow for complex non-conforming geometries as well as hybrid- andequi-dimensional models and discretizations of flow through fractured porousmedia. The variational transfer is based on the $L^2$-projection and enables anaccurate and highly efficient parallel projection of fields betweennon-conforming meshes (e.g.,\ between fracture and porous matrix domain). Wepresent the different techniques as a unified mathematical framework with apractical perspective. By means of numerical examples we discuss both,performance and applicability of the particular strategies. Comparisons offinite element simulation results to widely adopted 2D benchmark cases showgood agreement and the dual Lagrange multiplier spaces show good performance.In an extension to 3D fracture networks, we first provide complementary resultsto a recently developed benchmark case, before we explore a complex scenariowhich leverages the different types of fracture meshes. Complex and highlyconductive fracture networks are found more suitable in combination withembedded hybrid-dimensional fractures. However, thick and blocking fracturesare better approximated by equi-dimensional embedded fractures and theequi-dimensional mortar method, respectively.

Comparison and Application of non-Conforming Mesh Models for Flow in Fractured Porous Media using dual {L}agrange multipliers