A family of Multiscale Hybrid-Mixed finite element methods for the Darcy equation with rough coefficients

Keywords

Finite element method, Mathematics, Discretization, Piecewise, Boundary value problem

References

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• Mixed and Hybrid Finite Element MethodsFranco Brezzi, Michel Fortin — 2011
• Analysis of the DPG Method for the Poisson EquationLeszek Demkowicz, Jay Gopalakrishnan — 2011
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• Multiscale Hybrid-Mixed MethodRodolfo Araya, Christopher Harder, Diego Paredes — 2013
• Numerical multiscale methods for a reaction-dominated modelHonório Joaquim Fernando, Christopher Harder, Diego Paredes — 2012
• Primal hybrid finite element methods for 2nd order elliptic equationsPierre-Arnaud Raviart, J. M. Thomas — 1977
• Analysis of a Two-Scale, Locally Conservative Subgrid Upscaling for Elliptic ProblemsTodd Arbogast — 2004
• Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic ProblemsBernardo Cockburn, Jay Gopalakrishnan, Raytcho Lazarov — 2009
• A mixed multiscale finite element method for elliptic problems with oscillating coefficientsZhiming Chen, Thomas Y. Hou — 2003
• Multiscale finite element methods for high-contrast problems using local spectral basis functionsYalchin Efendiev, Juan Galvis, Xiaohui Wu — 2011
• Generalized Finite Element Methods: Their Performance and Their Relation to Mixed MethodsIvo Babuška, John E. Osborn — 1983
• On a Residual Local Projection Method for the Darcy EquationLeopoldo P. Franca, Christopher Harder, Frédéric Valentin — 2009
• A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous MediaThomas Y. Hou, Xiaohui Wu — 1997
• Calculation of Internodal Transmissivities in Finite Difference Models of Flow in Heterogeneous Porous MediaRégis Kruel Romeu, B. Nœtinger — 1995
• A new multiscale finite element method for high-contrast elliptic interface problemsC.-C. Chu, Ivan G. Graham, Tingzheng Hou — 2010

Cited by

• Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshesDaniele A. Di Pietro, Alexandre Ern — 2013
• A Review of Hybrid High-Order Methods: Formulations, Computational Aspects, Comparison with Other MethodsDaniele A. Di Pietro, Alexandre Ern, Simon Lemaire — 2016
• Multiscale Hybrid-Mixed MethodRodolfo Araya, Christopher Harder, Diego Paredes — 2013
• On a Multiscale Hybrid-Mixed Method for Advective-Reactive Dominated Problems with Heterogeneous CoefficientsChristopher Harder, Diego Paredes, Frédéric Valentin — 2015
• Abstract multiscale-hybrid-mixed methodsAlexandre L. Madureira — 2014
• Multi-scale modelling of geomechanical behaviour using the Voronoi cell finite element method (VCFEM) and finite-discrete element method (VCFEM-DEM)B. Karchewski — 2015
• Multiscale Hybrid-Mixed Method for Porous Media ProblemsDiego Paredes, Frédéric Valentin, Christopher Harder — 2013
• Investigation of a hybrid polygonal finite element formulation for confined and unconfined seepageBrandon Karchewski, Anna Pekinasova, Dieter Stolle — 2016
• Simulation of electromagnetic waves propagation in nano-optics with a high-order discontinuous Galerkin time-domain methodJonathan Viquerat — 2015
• On the robustness of multiscale hybrid-mixed methodsDiego Paredes, Frédéric Valentin, Henrique Versieux — 2016
• An enriched multiscale mortar space for high contrast flow problemsEric T. Chung, Shubin Fu, Yanfang Yang — 2016
• The Multiscale Hybrid-Mixed method for the Maxwell Equations in Heterogeneous MediaStéphane Lanteri, Diego Paredes, Claire Scheid — 2018
• A multiscale hybrid-mixed method for the Maxwell equations in the time domainStéphane Lanteri, Raphaël Léger, Diego Paredes — 2016
• On the Implementation of a Scalable Simulator for Multiscale Hybrid-Mixed MethodsAntônio Tadeu A. Gomes, Weslley da Silva Pereira, Frédéric Valentin — 2017
• A Locking-Free MHM Method for ElasticityWeslley da Silva Pereira, Frédéric Valentin — 2017
• FV-MHMM method for reservoir modelingJacques Franc, L. Jeannin, Gérald Debenest — 2017
• MHM methods for time dependent propagation of electromagnetics wavesStéphane Lanteri, Diego Paredes, Claire Scheid — 2015
• A residual-free bubble formulation for nonlinear elliptic problems with oscillatory coefficientsManuel Barreda, Alexandre L. Madureira — 2017
• A wrapper around parallel MUMPS solver to reduce its memory usage and execution time for finite element method computationsMaciej Paszyński, Antônio Tadeu A. Gomes — 2017
• Multiscale hybrid-mixed method for the Stokes and Brinkman equations—The methodRodolfo Araya, Christopher Harder, Abner H. Poza — 2017

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