A subcell-enriched Galerkin method for advection problems

In this work, we introduce a generalization of the enriched Galerkin (EG) method. The key feature of our scheme is an adaptive two-mesh approach that, in addition to the standard enrichment of a conforming finite element discretization via discontinuous degrees of freedom, allows to subdivide selected (e.g. troubled) mesh cells in a non-conforming fashion and to use further discontinuous enrichment on this finer submesh. We prove stability and sharp a priori error estimates for a linear advection equation by using a specially tailored projection and conducting some parts of a standard convergence analysis for both meshes. By allowing an arbitrary degree of enrichment on both, the coarse and the fine mesh (also including the case of no enrichment), our analysis technique is very general in the sense that our results cover the range from the standard continuous finite element method to the standard discontinuous Galerkin (DG) method with (or without) local subcell enrichment. Numerical experiments confirm our analytical results and indicate good robustness of the proposed method

Enriched mixed finite element models for dynamic analysis of continuous and fractured porous media

The final publication is available at Elsevier via https://dx.doi.org/10.1016/j.cma.2018.08.011 © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/Enriched Finite Element Models are presented to more accurately investigate the transient and wave propagation responses of continuous and fractured porous media based on mixture theory. Firstly, the Generalized Finite Element Method (GFEM) trigonometric enrichments are introduced to suppress the spurious oscillations that may appear in dynamic analysis with the regular Finite Element Method (FEM) due to numerical dispersion/Gibbs phenomenon. Secondly, the Phantom Node Method (PNM) is employed to model multiple arbitrary fractures independently of the mesh topology. Thirdly, frictional contact behavior is simulated using an Augmented Lagrange Multiplier technique. Mixed Lagrangian interpolants, bi-quadratic for displacements and bi-linear for pore pressure, are used for the underlying FEM basis functions. Transient (non-wave propagation) response of fractured porous media is effectively modeled using the PNM. Wave propagation in continuous porous media is effectively modeled using the mixed GFEM. Wave propagation in fractured porous media is simulated using a mixed GFEM-enriched Phantom Node Method (PNM-GFEM-M). The developed mixed GFEM portion of the model is verified through a transient consolidation problem. Subsequently, the ability of the enriched FEM models to capture the dynamic response of fractured fully-saturated porous media under mechanical and hydraulic stimulations is illustrated. The superior ability of the PNM-GFEM-M in inhibiting spurious oscillations is shown in comparison against the regular finite element solutions of some impact problems. It is demonstrated that by embedding appropriate enrichment basis functions in both displacement and pore pressure fields the results obtained are more accurate than those obtained using standard finite element approximations or approximations in which only the displacement is enriched.Natural Sciences and Engineering Research Council of Canad