Unified analysis of discontinuous Galerkin approximations of flows in fractured porous media on polygonal and polyhedral grids
We propose a unified formulation based on discontinuous Galerkin methods on polygonal/polyhedral grids for the simulation of flows in fractured porous media. We adopt a model for single-phase flows where the fracture is modeled as a (d-1)-dimensional interface in a d-dimensional bulk domain, and mod...
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| Published in: | Mathematics in engineering Vol. 2; no. 2; pp. 340 - 385 |
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01-01-2020
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| Abstract | We propose a unified formulation based on discontinuous Galerkin methods on polygonal/polyhedral grids for the simulation of flows in fractured porous media. We adopt a model for single-phase flows where the fracture is modeled as a (d-1)-dimensional interface in a d-dimensional bulk domain, and model the flow in the porous medium and in the fracture by means of the Darcy’s law. The two problems are then coupled through physically consistent conditions. We focus on the numerical approximation of the coupled bulk-fracture problem and present and analyze, in an unified setting, all the possible combinations of primal-primal, mixed-primal, primal-mixed and mixed-mixed formulations for the bulk and fracture problems, respectively. For all the possible combinations, we prove their well-posedness and derive a priori hp-version error estimates in a suitable (mesh-dependent) energy norm. Finally, preliminary numerical experiments assess the theoretical error estimates and accuracy of the proposed formulations. |
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| AbstractList | We propose a unified formulation based on discontinuous Galerkin methods on polygonal/polyhedral grids for the simulation of flows in fractured porous media. We adopt a model for single-phase flows where the fracture is modeled as a (d-1)-dimensional interface in a d-dimensional bulk domain, and model the flow in the porous medium and in the fracture by means of the Darcy’s law. The two problems are then coupled through physically consistent conditions. We focus on the numerical approximation of the coupled bulk-fracture problem and present and analyze, in an unified setting, all the possible combinations of primal-primal, mixed-primal, primal-mixed and mixed-mixed formulations for the bulk and fracture problems, respectively. For all the possible combinations, we prove their well-posedness and derive a priori hp-version error estimates in a suitable (mesh-dependent) energy norm. Finally, preliminary numerical experiments assess the theoretical error estimates and accuracy of the proposed formulations. |
| Author | Verani, Marco Facciolà, Chiara F. Antonietti, Paola |
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| CitedBy_id | crossref_primary_10_1016_j_camwa_2021_08_015 crossref_primary_10_1016_j_jcp_2023_112244 crossref_primary_10_1007_s10915_020_01372_0 crossref_primary_10_1016_j_matcom_2021_07_012 crossref_primary_10_1002_nme_6833 crossref_primary_10_1080_10584587_2022_2072118 crossref_primary_10_1007_s11075_023_01635_5 crossref_primary_10_1007_s10013_022_00566_3 |
| Cites_doi | 10.1137/17M1138194 10.1137/15M1008117 10.1016/j.jcp.2011.08.018 10.1016/j.finel.2015.10.003 10.1137/17M1119500 10.1090/S0025-5718-08-02123-6 10.1007/s10915-013-9792-y 10.1142/S0218202518500100 10.1016/j.procs.2011.04.102 10.1051/m2an/2015059 10.1051/m2an/2015079 10.1016/j.compfluid.2018.07.022 10.1016/S0045-7825(01)00260-2 10.1137/130947015 10.1007/s10915-018-0783-x 10.1007/s00158-011-0706-z 10.1142/S0218202514400028 10.1016/j.cma.2014.09.009 10.1137/13091141X 10.1007/s10596-007-9062-x 10.1007/s10092-017-0223-6 10.1137/070706616 10.1090/S0025-5718-08-02146-7 10.1016/j.cma.2014.07.016 10.1090/S0025-5718-10-02334-3 10.1016/j.advwatres.2013.04.001 10.1007/s10915-010-9390-1 10.1137/040613950 10.1137/16M1073285 10.1051/m2an/2008052 10.1137/S0036142900371003 10.1142/S0218202505000832 10.1142/S0218202506001157 10.1016/j.cma.2008.12.033 10.1023/A:1015118613130 10.1016/j.cma.2007.08.013 10.1051/m2an/2015067 10.1002/nme.1141 10.1051/m2an/2017028 10.1006/jcph.1996.5633 10.1137/S1064827503429363 10.1137/0715010 10.1016/S0045-7825(02)00371-7 10.1137/S0036142997316712 10.1142/S0218202514500146 10.1051/m2an/2015087 10.1142/S0218202516500160 10.1016/j.compfluid.2011.11.002 10.1051/m2an/2011148 10.1016/j.cma.2018.08.012 10.1007/s002110050248 10.1137/0719052 10.1051/m2an/2015090 10.1142/S0218202512500492 10.1137/120877246 |
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| References | Beirão da Veiga L, Brezzi F, Marini L, et al. (14) 45 46 Formaggia L, Scotti A, Sottocasa F (52) Benedetto MF, Berrone S, Pieraccini S, et al. (53) Antonietti PF, da Veiga LB, Mora D, et al. (15) Hyman J, Shashkov M, Steinberg S (3) Frih N, Roberts JE, Saada A (48) Cockburn B, Gopalakrishnan J, Sayas FJ (24) Benedetto MF, Berrone S, Scialò S (54) Antonietti PF, Facciolà C, Russo A, et al. (59) 12 Sukumar N, Tabarraei A (9) 57 Perugia I, Schötzau D (69) 18 Chave FA, Di Pietro D, Formaggia L (55) Antonietti PF, Sarti M, Verani M (60) Cockburn B, Gopalakrishnan J, Lazarov R (23) Antonietti PF, Formaggia L, Scotti A, et al. (8) Di Pietro DA, Ern A (19) D'Angelo C, Scotti A (56) Cockburn B, Shu CW (66) 2 Burman E, Hansbo P, Larson MG, et al. (58) Ayuso de Dios B, Lipnikov K, Manzini G (29) Beirão da Veiga L, Brezzi F, Marini LD, et al. (16) 7 Cangiani A, Dong Z, Georgoulis EH, et al. (37) Cangiani A, Dong Z, Georgoulis EH (38) 62 Beirão da Veiga L, Brezzi F, Cangiani A, et al. (13) 63 Wheeler MF (64) 20 Fumagalli A, Scotti A (49) Arnold DN (65) 21 Antonietti PF, Pennesi G (44) 68 Castillo P, Cockburn B, Perugia I, et al. (67) Cockburn B, Dond B, Guzmán J (22) Antonietti PF, Mazzieri I (42) Dolbow J, Moës N, Belytschko T (10) Masud A, Hughes TJ (61) Tabarraei A, Sukumar N (11) 70 Bassi F, Botti L, Colombo A (35) Cangiani A, Georgoulis EH, Houston P (36) Hackbusch W, Sauter SA (1) 72 Brezzi F, Lipnikov K, Shashkov M (6) Antonietti PF, Giani S, Houston P (26) 30 74 Bassi F, Botti L, Colombo A, et al. (33) 75 Cockburn B, Guzmán J, Wang H (25) 76 77 78 Martin V, Jaffré J, Roberts JE (47) Jaffré J, Mnejja M, Roberts J (50) Angot P, Boyer F, Hubert F (51) Brezzi F, Lipnikov K, Simoncini V (4) Antonietti PF, Manzini G, Verani M (28) Antonietti PF, Houston P, Hu X, et al. (39) Droniou J, Eymard R, Herbin R (31) Antonietti PF, Brezzi F, Marini LD (32) Talischi C, Paulino GH, Pereira A, et al. (73) Antonietti PF, Houston P (71) Brezzi F, Lipnikov K, Shashkov M (5) Antonietti PF, da Veiga LB, Scacchi S, et al. (17) Antonietti PF, Giani S, Houston P (27) 40 41 Bassi F, Botti L, Colombo A, et al. (34) 43 |
| References_xml | – ident: 59 article-title: Discontinuous Galerkin approximation of flows in fractured porous media on polytopic grids publication-title: SIAM J Sci Comput doi: 10.1137/17M1138194 contributor: fullname: Antonietti PF, Facciolà C, Russo A, et al. – ident: 17 article-title: A C1 virtual element method for the CahnHilliard equation with polygonal meshes publication-title: SIAM J Numer Anal doi: 10.1137/15M1008117 contributor: fullname: Antonietti PF, da Veiga LB, Scacchi S, et al. – ident: 33 article-title: On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations publication-title: J Comput Phys doi: 10.1016/j.jcp.2011.08.018 contributor: fullname: Bassi F, Botti L, Colombo A, et al. – ident: 54 article-title: A globally conforming method for solving flow in discrete fracture networks using the virtual element method publication-title: Finite Elem Anal Des doi: 10.1016/j.finel.2015.10.003 contributor: fullname: Benedetto MF, Berrone S, Scialò S – ident: 55 article-title: A hybrid high-order method for Darcy flows in fractured porous media publication-title: SIAM J Sci Comput doi: 10.1137/17M1119500 contributor: fullname: Chave FA, Di Pietro D, Formaggia L – ident: 22 article-title: A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems publication-title: Math Comput doi: 10.1090/S0025-5718-08-02123-6 contributor: fullname: Cockburn B, Dond B, Guzmán J – ident: 27 article-title: Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains publication-title: J Sci Comput doi: 10.1007/s10915-013-9792-y contributor: fullname: Antonietti PF, Giani S, Houston P – ident: 68 article-title: The hp-local discontinuous galerkin method for low-frequency time-harmonic maxwell equations – ident: 76 article-title: Preconditioning techniques for the numerical solution of flow in fractured porous media – ident: 28 article-title: The fully nonconforming virtual element method for biharmonic problems publication-title: Math Mod Meth Appl S doi: 10.1142/S0218202518500100 contributor: fullname: Antonietti PF, Manzini G, Verani M – ident: 41 article-title: hp-Version Discontinuous Galerkin Methods on Polytopic Meshes, Springer International Publishing – ident: 50 article-title: A discrete fracture model for two-phase flow with matrix-fracture interaction publication-title: Procedia Comput Sci doi: 10.1016/j.procs.2011.04.102 contributor: fullname: Jaffré J, Mnejja M, Roberts J – ident: 37 article-title: hp-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes publication-title: ESAIM Math Model Numer Anal doi: 10.1051/m2an/2015059 contributor: fullname: Cangiani A, Dong Z, Georgoulis EH, et al. – ident: 31 article-title: Gradient schemes: Generic tools for the numerical analysis of diffusion equations publication-title: ESAIM Math Model Numer Anal doi: 10.1051/m2an/2015079 contributor: fullname: Droniou J, Eymard R, Herbin R – ident: 58 article-title: Cut finite elements for convection in fractured domains publication-title: Comput Fluids doi: 10.1016/j.compfluid.2018.07.022 contributor: fullname: Burman E, Hansbo P, Larson MG, et al. – ident: 10 article-title: An extended finite element method for modeling crack growth with frictional contact publication-title: Comput Method Appl M doi: 10.1016/S0045-7825(01)00260-2 contributor: fullname: Dolbow J, Moës N, Belytschko T – ident: 60 article-title: Multigrid algorithms for hp-discontinuous Galerkin discretizations of elliptic problems publication-title: SIAM J Numer Anal doi: 10.1137/130947015 contributor: fullname: Antonietti PF, Sarti M, Verani M – ident: 78 article-title: An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids – ident: 44 article-title: V-cycle multigrid algorithms for discontinuous Galerkin methods on non-nested polytopic meshes publication-title: J Sci Comput doi: 10.1007/s10915-018-0783-x contributor: fullname: Antonietti PF, Pennesi G – ident: 73 article-title: Polymesher: A general-purpose mesh generator for polygonal elements written in matlab publication-title: Struct Multidiscip O doi: 10.1007/s00158-011-0706-z contributor: fullname: Talischi C, Paulino GH, Pereira A, et al. – ident: 35 article-title: Agglomeration-based physical frame dG discretizations: An attempt to be mesh free publication-title: Math Mod Meth Appl S doi: 10.1142/S0218202514400028 contributor: fullname: Bassi F, Botti L, Colombo A – ident: 70 article-title: An analysis of the finite element method, Prentice-Hall Englewood Cliffs – ident: 19 article-title: A hybrid high-order locking-free method for linear elasticity on general meshes publication-title: Comput Meth Appl Mech Eng doi: 10.1016/j.cma.2014.09.009 contributor: fullname: Di Pietro DA, Ern A – ident: 15 article-title: A stream virtual element formulation of the Stokes problem on polygonal meshes publication-title: SIAM J Numer Anal doi: 10.1137/13091141X contributor: fullname: Antonietti PF, da Veiga LB, Mora D, et al. – ident: 48 article-title: Modeling fractures as interfaces: A model for Forchheimer fractures publication-title: Comput Geosci doi: 10.1007/s10596-007-9062-x contributor: fullname: Frih N, Roberts JE, Saada A – ident: 39 article-title: Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes publication-title: Calcolo doi: 10.1007/s10092-017-0223-6 contributor: fullname: Antonietti PF, Houston P, Hu X, et al. – ident: 74 article-title: Gradient discretization of hybrid-dimensional Darcy flow in fractured porous media with discontinuous pressures at matrix-fracture interfaces – ident: 23 article-title: Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems publication-title: SIAM J Numer Anal doi: 10.1137/070706616 contributor: fullname: Cockburn B, Gopalakrishnan J, Lazarov R – ident: 25 article-title: Superconvergent discontinuous Galerkin methods for second-order elliptic problems publication-title: Math Comput doi: 10.1090/S0025-5718-08-02146-7 contributor: fullname: Cockburn B, Guzmán J, Wang H – ident: 53 article-title: The virtual element method for discrete fracture network simulations publication-title: Comput Meths Appl Mech Eng doi: 10.1016/j.cma.2014.07.016 contributor: fullname: Benedetto MF, Berrone S, Pieraccini S, et al. – ident: 24 article-title: A projection-based error analysis of HDG methods publication-title: Math Comput doi: 10.1090/S0025-5718-10-02334-3 contributor: fullname: Cockburn B, Gopalakrishnan J, Sayas FJ – ident: 49 article-title: A numerical method for two-phase flow in fractured porous media with non-matching grids publication-title: Adv Water Resour doi: 10.1016/j.advwatres.2013.04.001 contributor: fullname: Fumagalli A, Scotti A – ident: 30 article-title: Conforming and nonconforming virtual element methods for elliptic problems – ident: 63 article-title: (2001/02) Unified analysis of discontinuous Galerkin methods for elliptic problems – ident: 71 article-title: A class of domain decomposition preconditioners for hpdiscontinuous Galerkin finite element methods publication-title: J Sci Comput doi: 10.1007/s10915-010-9390-1 contributor: fullname: Antonietti PF, Houston P – ident: 5 article-title: Convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes publication-title: SIAM J Numer Anal doi: 10.1137/040613950 contributor: fullname: Brezzi F, Lipnikov K, Shashkov M – ident: 38 article-title: hp-version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes publication-title: SIAM J Sci Comput doi: 10.1137/16M1073285 contributor: fullname: Cangiani A, Dong Z, Georgoulis EH – ident: 51 article-title: Asymptotic and numerical modelling of flows in fractured porous media publication-title: M2AN Math Model Numer Anal doi: 10.1051/m2an/2008052 contributor: fullname: Angot P, Boyer F, Hubert F – ident: 67 article-title: An a priori error analysis of the local discontinuous Galerkin method for elliptic problems publication-title: SIAM J Numer Anal doi: 10.1137/S0036142900371003 contributor: fullname: Castillo P, Cockburn B, Perugia I, et al. – ident: 77 article-title: Preconditioning high-order discontinuous galerkin discretizations of elliptic problems – ident: 4 article-title: A family of Mimetic finite difference methods on polygonal and polyhedral meshes publication-title: Math Mod Meth Appl S doi: 10.1142/S0218202505000832 contributor: fullname: Brezzi F, Lipnikov K, Simoncini V – ident: 6 article-title: Convergence of mimetic finite difference method for diffusion problems on polyhedral meshes with curved faces publication-title: Math Mod Meth Appl S doi: 10.1142/S0218202506001157 contributor: fullname: Brezzi F, Lipnikov K, Shashkov M – ident: 32 article-title: Bubble stabilization of discontinuous Galerkin methods publication-title: Comput Meth Appl Mech Eng doi: 10.1016/j.cma.2008.12.033 contributor: fullname: Antonietti PF, Brezzi F, Marini LD – ident: 69 article-title: An hp-analysis of the local discontinuous galerkin method for diffusion problems publication-title: J Sci Comput doi: 10.1023/A:1015118613130 contributor: fullname: Perugia I, Schötzau D – ident: 11 article-title: Extended finite element method on polygonal and quadtree meshes publication-title: Comput Method Appl M doi: 10.1016/j.cma.2007.08.013 contributor: fullname: Tabarraei A, Sukumar N – ident: 46 article-title: Modeling fractures as interfaces for flow and transport in porous media – ident: 16 article-title: Mixed virtual element methods for general second order elliptic problems on polygonal meshes publication-title: ESAIM Math Model Numer Anal doi: 10.1051/m2an/2015067 contributor: fullname: Beirão da Veiga L, Brezzi F, Marini LD, et al. – ident: 40 article-title: Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains, In: Lecture Notes in Computational Science and Engineering, Springer, 281-310 – ident: 9 article-title: Conforming Polygonal Finite Elements publication-title: Int J Numer Meth Eng doi: 10.1002/nme.1141 contributor: fullname: Sukumar N, Tabarraei A – ident: 12 article-title: The extended/generalized finite element method: An overview of the method and its applications – ident: 18 article-title: An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators – ident: 52 article-title: Analysis of a mimetic finite difference approximation of flows in fractured porous media publication-title: ESAIM Math Model Numer Anal doi: 10.1051/m2an/2017028 contributor: fullname: Formaggia L, Scotti A, Sottocasa F – ident: 62 article-title: Mixed discontinuous Galerkin methods for darcy flow – ident: 21 article-title: A review of hybrid high-order methods: Formulations, computational aspects, comparison with other methods – ident: 3 article-title: The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials publication-title: J Comput Phys doi: 10.1006/jcph.1996.5633 contributor: fullname: Hyman J, Shashkov M, Steinberg S – ident: 47 article-title: Modeling fractures and barriers as interfaces for flow in porous media publication-title: SIAM J Sci Comput doi: 10.1137/S1064827503429363 contributor: fullname: Martin V, Jaffré J, Roberts JE – ident: 64 article-title: An elliptic collocation-finite element method with interior penalties publication-title: SIAM J Numer Anal doi: 10.1137/0715010 contributor: fullname: Wheeler MF – ident: 7 article-title: The Mimetic Finite Difference Method for Elliptic Problems, Cham: Springer – ident: 20 article-title: Hybrid high-order methods for variable-diffusion problems on general meshes – ident: 61 article-title: A stabilized mixed finite element method for darcy flow publication-title: Comput Meth Appl Mech Eng doi: 10.1016/S0045-7825(02)00371-7 contributor: fullname: Masud A, Hughes TJ – ident: 66 article-title: The local discontinuous Galerkin method for time-dependent convection-diffusion systems publication-title: SIAM J Numer Anal doi: 10.1137/S0036142997316712 contributor: fullname: Cockburn B, Shu CW – ident: 36 article-title: hp-version discontinuous Galerkin methods on polygonal and polyhedral meshes publication-title: Math Mod Meth Appl S doi: 10.1142/S0218202514500146 contributor: fullname: Cangiani A, Georgoulis EH, Houston P – ident: 8 article-title: Mimetic finite difference approximation of flows in fractured porous media publication-title: ESAIM Math Model Numer Anal doi: 10.1051/m2an/2015087 contributor: fullname: Antonietti PF, Formaggia L, Scotti A, et al. – ident: 14 article-title: Virtual element method for general second-order elliptic problems on polygonal meshes publication-title: Math Mod Meth Appl S doi: 10.1142/S0218202516500160 contributor: fullname: Beirão da Veiga L, Brezzi F, Marini L, et al. – ident: 34 article-title: Agglomeration based discontinuous Galerkin discretization of the Euler and Navier-Stokes equations publication-title: Comput Fluids doi: 10.1016/j.compfluid.2011.11.002 contributor: fullname: Bassi F, Botti L, Colombo A, et al. – ident: 56 article-title: A mixed finite element method for darcy flow in fractured porous media with non-matching grids publication-title: ESAIM Math Mod Numer Anal doi: 10.1051/m2an/2011148 contributor: fullname: D'Angelo C, Scotti A – ident: 42 article-title: High-order discontinuous Galerkin methods for the elastodynamics equation on polygonal and polyhedral meshes publication-title: Comput Meth Appl Mech Eng doi: 10.1016/j.cma.2018.08.012 contributor: fullname: Antonietti PF, Mazzieri I – ident: 57 article-title: A review of the XFEM-based approximation of flow in fractured porous media – ident: 75 article-title: Polytopic discontinuous Galerkin methods for the numerical modelling of flow in porous media with networks of intersecting fractures – ident: 1 article-title: Composite finite elements for the approximation of PDEs on domains with complicated micro-structures publication-title: Numer Math doi: 10.1007/s002110050248 contributor: fullname: Hackbusch W, Sauter SA – ident: 65 article-title: An interior penalty finite element method with discontinuous elements publication-title: SIAM J Numer Anal doi: 10.1137/0719052 contributor: fullname: Arnold DN – ident: 29 article-title: The nonconforming virtual element method publication-title: ESAIM Math Model Numer Anal doi: 10.1051/m2an/2015090 contributor: fullname: Ayuso de Dios B, Lipnikov K, Manzini G – ident: 72 article-title: Singular integrals and differentiability properties of functions, Princeton university press – ident: 13 article-title: Basic principles of virtual element methods publication-title: Math Mod Meth Appl S doi: 10.1142/S0218202512500492 contributor: fullname: Beirão da Veiga L, Brezzi F, Cangiani A, et al. – ident: 43 article-title: A high-order discontinuous galerkin approach to the elasto-acoustic problem – ident: 2 article-title: Composite finite elements for problems containing small geometric details – ident: 26 article-title: hp-version composite discontinuous Galerkin methods for elliptic problems on complicated domains publication-title: SIAM J Sci Comput doi: 10.1137/120877246 contributor: fullname: Antonietti PF, Giani S, Houston P – ident: 45 article-title: Domain decomposition for some transmission problems in flow in porous media |
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