Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

An Interior Penalty Discontinuous Galerkin Method for an Interface Model of Flow in Fractured Porous Media

Yong Liu and Ziyao Xu
Journal of Scientific Computing 107 (3) (2026)
https://doi.org/10.1007/s10915-026-03285-w

Hierarchical discontinuous Galerkin method for reduced karst conduit-flow in carbonate porous media

Igor Mozolevski, Luciane A. Schuh, Edson L. Valmorbida, Marcio A. Murad and Josue Barroso
Mathematics and Computers in Simulation 248 440 (2026)
https://doi.org/10.1016/j.matcom.2026.04.015

An implicit-explicit scheme and adaptive multiscale approximation of generalized Forchheimer flow in fractured porous media

Maria Vasilyeva, Nana Adjoah Mbroh, Denis Spiridonov and Tatiana Timofeeva
Computers & Mathematics with Applications 211 1 (2026)
https://doi.org/10.1016/j.camwa.2026.02.015

Multiscale discrete fracture-matrix method for simulating groundwater flow in fractured geological media

Chen Zuo, Lei Ma, Di Gao, Qiankun Luo, Yaping Deng and Jiazhong Qian
Journal of Hydrology 675 135583 (2026)
https://doi.org/10.1016/j.jhydrol.2026.135583

A 3D-1D virtual element method for modeling root water uptake

Stefano Berrone, Stefano Ferraris, Denise Grappein, Gioana Teora and Fabio Vicini
Computers & Mathematics with Applications 213 22 (2026)
https://doi.org/10.1016/j.camwa.2026.03.027

A cut finite element method for the Biot system of poroelasticity

Nanna Berre, Kent-Andre Mardal, André Massing and Ivan Yotov
Computer Methods in Applied Mechanics and Engineering 458 119048 (2026)
https://doi.org/10.1016/j.cma.2026.119048

Mixed finite element method for nonlinear hybrid-dimensional fracture model with varying aperture

Fei Sun and Hongxing Rui
Applied Mathematics Letters 177 109878 (2026)
https://doi.org/10.1016/j.aml.2026.109878

Numerical Manifold Method of Fluid Flow in Fractured Porous Media: Emphasizing Flow along and across Fractures

Xi-long Li and Hong Zhang
Computers and Geotechnics 187 107522 (2025)
https://doi.org/10.1016/j.compgeo.2025.107522

Conservation properties of non-conforming embedded finite-element methods based on lagrange multipliers

Maria Giuseppina Chiara Nestola, Patrick Zulian, Marco Favino and Rolf Krause
BIT Numerical Mathematics 65 (3) (2025)
https://doi.org/10.1007/s10543-025-01075-8

Estimation of uncertainties in the density driven flow in fractured porous media using MLMC

Dmitry Logashenko, Alexander Litvinenko, Raul Tempone and Gabriel Wittum
Engineering with Computers 41 (6) 4109 (2025)
https://doi.org/10.1007/s00366-024-02089-6

An extension of the box method discrete fracture model (Box-DFM) to include low-permeable barriers with minimal additional degrees of freedom

Ziyao Xu and Dennis Gläser
Advances in Water Resources 195 104869 (2025)
https://doi.org/10.1016/j.advwatres.2024.104869

Fluid flow analysis of discrete fracture networks using a locally conservative stable mixed finite element method

Nathan Shauer, José B. Villegas S., Bernd Flemisch and Philippe R. B. Devloo
Computational Geosciences 29 (2) (2025)
https://doi.org/10.1007/s10596-025-10358-6

Analysis of divergence-preserving unfitted finite element methods for the mixed Poisson problem

Christoph Lehrenfeld, Tim van Beeck and Igor Voulis
Mathematics of Computation 94 (354) 1667 (2024)
https://doi.org/10.1090/mcom/4027

A Stokes–Darcy–Darcy model and its discontinuous Galerkin method on polytopic grids

Rui Li, Yali Gao, Chen-Song Zhang and Zhangxin Chen
Journal of Computational Physics 501 112780 (2024)
https://doi.org/10.1016/j.jcp.2024.112780

A mixed‐dimensional model for direct current simulations in the presence of a thin high‐resistivity liner

Alessio Fumagalli, Lorenzo Panzeri, Luca Formaggia, Anna Scotti and Diego Arosio
International Journal for Numerical Methods in Engineering 125 (6) (2024)
https://doi.org/10.1002/nme.7407

A space-time mixed finite element method for reduced fracture flow models on nonmatching grids

Thi-Thao-Phuong Hoang and Ivan Yotov
Mathematics of Computation 94 (356) 2645 (2024)
https://doi.org/10.1090/mcom/4031

Hydraulic fracturing based extraction for remediation of contaminated aquitards considering nonlinear and nonequilibrium sorption: A mathematical model

Shi-Jin Feng and Xiang-Hong Ding
Computers and Geotechnics 173 106574 (2024)
https://doi.org/10.1016/j.compgeo.2024.106574

Application of deep learning reduced-order modeling for single-phase flow in faulted porous media

Enrico Ballini, Luca Formaggia, Alessio Fumagalli, Anna Scotti and Paolo Zunino
Computational Geosciences 28 (6) 1279 (2024)
https://doi.org/10.1007/s10596-024-10320-y

An extended nonconforming finite element method for the coupled Darcy–Stokes problem

Pei Cao and Jinru Chen
Journal of Computational and Applied Mathematics 451 116092 (2024)
https://doi.org/10.1016/j.cam.2024.116092

A Divergence Preserving Cut Finite Element Method for Darcy Flow

Thomas Frachon, Peter Hansbo, Erik Nilsson and Sara Zahedi
SIAM Journal on Scientific Computing 46 (3) A1793 (2024)
https://doi.org/10.1137/22M149702X

A numerical investigation on coupling of conforming and hybridizable interior penalty discontinuous Galerkin methods for fractured groundwater flow problems

Grégory Etangsale, Marwan Fahs, Vincent Fontaine and Hussein Hoteit
Mathematics and Computers in Simulation 221 435 (2024)
https://doi.org/10.1016/j.matcom.2024.03.003

A discrete fracture-matrix approach based on Petrov-Galerkin immersed finite element for fractured porous media flow on nonconforming mesh

Jijing Zhao and Hongxing Rui
Journal of Computational Physics 499 112718 (2024)
https://doi.org/10.1016/j.jcp.2023.112718

The MLS-based numerical manifold method for Darcy flow in heterogeneous porous media

Yuanqiang Chen, Hong Zheng, Boyuan Yin and Wei Li
Engineering Analysis with Boundary Elements 148 220 (2023)
https://doi.org/10.1016/j.enganabound.2022.12.030

Fast and Robust Prediction of Multiphase Flow in Complex Fractured Reservoir Using a Fourier Neural Operator

Tie Kuang, Jianqiao Liu, Zhilin Yin, et al.
Energies 16 (9) 3765 (2023)
https://doi.org/10.3390/en16093765

A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media

Aleksei Tyrylgin, Maria Vasilyeva, Anatoly Alikhanov and Dongwoo Sheen
Journal of Computational and Applied Mathematics 418 114670 (2023)
https://doi.org/10.1016/j.cam.2022.114670

An Online Generalized Multiscale Finite Element Method for Dual-continuum Unsaturated Filtration Problem in Domains with Rough Boundaries

D. A. Spiridonov and J. Huang
Lobachevskii Journal of Mathematics 44 (10) 4170 (2023)
https://doi.org/10.1134/S1995080223100396

Modeling density-driven flow and solute transport in heterogeneous reservoirs with micro/macro fractures

A.R. Khoei, S.M. Mousavi and N. Hosseini
Advances in Water Resources 182 104571 (2023)
https://doi.org/10.1016/j.advwatres.2023.104571

Reduced flow model and transmissibility upscaling in multi-layered faulted reservoirs

Eduardo S. Castro, Josué S. Barroso, Marcio A. Murad and João N.C. Guerreiro
Computers & Geosciences 180 105439 (2023)
https://doi.org/10.1016/j.cageo.2023.105439

Polytopic discontinuous Galerkin methods for the numerical modelling of flow in porous media with networks of intersecting fractures

Paola F. Antonietti, Chiara Facciolà and Marco Verani
Computers & Mathematics with Applications 116 116 (2022)
https://doi.org/10.1016/j.camwa.2021.08.015

Thermal-Mechanical Coupling Model Based on the Hybrid Finite Element Method for Solving Bipolar the Plate Deformation of Hydrogen Fuel Cells

Wenxing Chen, Shuyang Dai and Baojuan Zheng
Machines 10 (7) 505 (2022)
https://doi.org/10.3390/machines10070505

Modeling the hydrodynamic behavior of fractures and barriers in porous media using coupling finite elements

Murilo Camargo, Pedro R. Cleto, Michael A. Maedo, Eduardo A. Rodrigues, Luís A.G. Bitencourt and Osvaldo L. Manzoli
Journal of Petroleum Science and Engineering 208 109700 (2022)
https://doi.org/10.1016/j.petrol.2021.109700

Two mixed finite element formulations for the weak imposition of the Neumann boundary conditions for the Darcy flow

Erik Burman and Riccardo Puppi
Journal of Numerical Mathematics 30 (2) 141 (2022)
https://doi.org/10.1515/jnma-2021-0042

Staggered DG Method with Small Edges for Darcy Flows in Fractured Porous Media

Lina Zhao, Dohyun Kim, Eun-Jae Park and Eric Chung
Journal of Scientific Computing 90 (3) (2022)
https://doi.org/10.1007/s10915-022-01760-8

Comparison and application of non-conforming mesh models for flow in fractured porous media using dual Lagrange multipliers

Patrick Zulian, Philipp Schädle, Liudmila Karagyaur and Maria G.C. Nestola
Journal of Computational Physics 449 110773 (2022)
https://doi.org/10.1016/j.jcp.2021.110773

Finite Element Modeling of Diffusion in Fractured Porous Media by Using Hierarchical Material Properties

G. D. Beskardes, C. J. Weiss, K. L. Kuhlman and K. W. Chang
Water Resources Research 58 (2) (2022)
https://doi.org/10.1029/2020WR029510

An extended finite element method for coupled Darcy–Stokes problems

Pei Cao and Jinru Chen
International Journal for Numerical Methods in Engineering 123 (19) 4586 (2022)
https://doi.org/10.1002/nme.7047

An arbitrary order Mixed Virtual Element formulation for coupled multi-dimensional flow problems

M.F. Benedetto, A. Borio, F. Kyburg, J. Mollica and S. Scialò
Computer Methods in Applied Mechanics and Engineering 391 114204 (2022)
https://doi.org/10.1016/j.cma.2021.114204

Multi-scale modelling of gas transport and production evaluation in shale reservoir considering crisscrossing fractures

Marembo Micheal, WenLong Xu, HengYu Xu, JiaNing Zhang, HongJie Jin, Hao Yu and HengAn Wu
Journal of Natural Gas Science and Engineering 95 104156 (2021)
https://doi.org/10.1016/j.jngse.2021.104156

Discontinuous finite volume element method for Darcy flows in fractured porous media

Rui Li, Yongchao Zhang, Jianhua Wu and Zhangxin Chen
Journal of Computational and Applied Mathematics 381 113025 (2021)
https://doi.org/10.1016/j.cam.2020.113025

Discontinuous and continuous Galerkin methods for compressible single-phase and two-phase flow in fractured porous media

Tianran Ma, Keni Zhang, Weijun Shen, Chaobin Guo and Hao Xu
Advances in Water Resources 156 104039 (2021)
https://doi.org/10.1016/j.advwatres.2021.104039

Discretization of Poisson’s equation in two domains with non algebraic interface conditions for plasma simulations

Andrea Villa, Luca Barbieri, Roberto Malgesini and Giacomo Buccella
Applied Mathematics and Computation 403 126179 (2021)
https://doi.org/10.1016/j.amc.2021.126179

Numerical upscaling for heterogeneous materials in fractured domains

Fredrik Hellman, Axel Målqvist and Siyang Wang
ESAIM: Mathematical Modelling and Numerical Analysis 55 S761 (2021)
https://doi.org/10.1051/m2an/2020061

Robust Linear Domain Decomposition Schemes for Reduced Nonlinear Fracture Flow Models

Elyes Ahmed, Alessio Fumagalli, Ana Budiša, et al.
SIAM Journal on Numerical Analysis 59 (1) 583 (2021)
https://doi.org/10.1137/19M1268392

Computational Implementation of a Mixed-Dimensional Model of Heat Transfer in the Soil–Pipe System in Cryolithic Zone

V. I. Vasil’ev, M. V. Vasil’eva, D. Ya. Nikiforov, et al.
Computational Mathematics and Mathematical Physics 61 (12) 2054 (2021)
https://doi.org/10.1134/S0965542521120162

Comparison of the response to geometrical complexity of methods for unstationary simulations in discrete fracture networks with conforming, polygonal, and non-matching grids

Andrea Borio, Alessio Fumagalli and Stefano Scialò
Computational Geosciences 25 (1) 143 (2021)
https://doi.org/10.1007/s10596-020-09996-9

Polyhedral Methods in Geosciences

Paola F. Antonietti, Chiara Facciolà, Paul Houston, et al.
SEMA SIMAI Springer Series, Polyhedral Methods in Geosciences 27 159 (2021)
https://doi.org/10.1007/978-3-030-69363-3_5

An implementation of mimetic finite difference method for fractured reservoirs using a fully implicit approach and discrete fracture models

Na Zhang and Ahmad S. Abushaikha
Journal of Computational Physics 446 110665 (2021)
https://doi.org/10.1016/j.jcp.2021.110665

Development and application of three-dimensional discrete fracture network modeling approach for fluid flow in fractured rock masses

Na Huang, Richeng Liu, Yujing Jiang and Yuanfang Cheng
Journal of Natural Gas Science and Engineering 91 103957 (2021)
https://doi.org/10.1016/j.jngse.2021.103957

Demonstration and application of NMM‐based fractured porous medium flow model

Qi‐Hua Zhang, Shao‐Zhong Lin, Hai‐Dong Su and Gen‐Hua Shi
International Journal for Numerical and Analytical Methods in Geomechanics 45 (1) 132 (2021)
https://doi.org/10.1002/nag.3154

Modeling the closure behavior of natural fractures in porous media using high aspect ratio interface elements

Heber A. Fabbri, Pedro R. Cleto, Aldo T. Gaiotto, Eduardo A. Rodrigues, Michael A. Maedo and Osvaldo L. Manzoli
Journal of Petroleum Science and Engineering 196 107979 (2021)
https://doi.org/10.1016/j.petrol.2020.107979

Generalized Multiscale Finite Element Method for the poroelasticity problem in multicontinuum media

Aleksei Tyrylgin, Maria Vasilyeva, Denis Spiridonov and Eric T. Chung
Journal of Computational and Applied Mathematics 374 112783 (2020)
https://doi.org/10.1016/j.cam.2020.112783

Unified analysis of discontinuous Galerkin approximations of flows in fractured porous media on polygonal and polyhedral grids

Paola F. Antonietti, Chiara Facciolà and Marco Verani
Mathematics in Engineering 2 (2) 340 (2020)
https://doi.org/10.3934/mine.2020017

A multi-layer reduced model for flow in porous media with a fault and surrounding damage zones

Alessio Fumagalli and Anna Scotti
Computational Geosciences 24 (3) 1347 (2020)
https://doi.org/10.1007/s10596-020-09954-5

Extensions of a coarse–fine mesh stabilized Schwarz alternating iteration domain decomposition method

Owe Axelsson
Journal of Computational and Applied Mathematics 364 112341 (2020)
https://doi.org/10.1016/j.cam.2019.112341

A phase field based discrete fracture model (PFDFM) for fluid flow in fractured porous media

Qingdong Zeng, Wenzheng Liu, Jun Yao and Jianlin Liu
Journal of Petroleum Science and Engineering 191 107191 (2020)
https://doi.org/10.1016/j.petrol.2020.107191

Generalized Multiscale Finite Element method for multicontinua unsaturated flow problems in fractured porous media

Denis Spiridonov, Maria Vasilyeva and Eric T. Chung
Journal of Computational and Applied Mathematics 370 112594 (2020)
https://doi.org/10.1016/j.cam.2019.112594

Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples

Alessio Fumagalli and Anna Scotti
Springer Proceedings in Mathematics & Statistics, Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples 323 55 (2020)
https://doi.org/10.1007/978-3-030-43651-3_4

Three dimensional simulation of the dynamics of electro active polymers using shell elements

Andrea Villa, Luca Barbieri and Roberto Malgesini
Applied Mathematics and Computation 377 125160 (2020)
https://doi.org/10.1016/j.amc.2020.125160

A Machine-Learning based generalization for an iterative Hybrid Embedded Fracture scheme

Sahar Z. Amir, Shuyu Sun and Mary F. Wheeler
Journal of Petroleum Science and Engineering 194 107235 (2020)
https://doi.org/10.1016/j.petrol.2020.107235

A mixed-dimensional CutFEM methodology for the simulation of fibre-reinforced composites

P. Kerfriden, S. Claus and I. Mihai
Advanced Modeling and Simulation in Engineering Sciences 7 (1) (2020)
https://doi.org/10.1186/s40323-020-00154-5

Stabilized Cut Discontinuous Galerkin Methods for Advection-Reaction Problems

Ceren Gürkan, Simon Sticko and André Massing
SIAM Journal on Scientific Computing 42 (5) A2620 (2020)
https://doi.org/10.1137/18M1206461

Learning macroscopic parameters in nonlinear multiscale simulations using nonlocal multicontinua upscaling techniques

Maria Vasilyeva, Wing T. Leung, Eric T. Chung, Yalchin Efendiev and Mary Wheeler
Journal of Computational Physics 412 109323 (2020)
https://doi.org/10.1016/j.jcp.2020.109323

Finite volume discretization for poroelastic media with fractures modeled by contact mechanics

Runar L. Berge, Inga Berre, Eirik Keilegavlen, Jan M. Nordbotten and Barbara Wohlmuth
International Journal for Numerical Methods in Engineering 121 (4) 644 (2020)
https://doi.org/10.1002/nme.6238

Numerical analysis of a two-phase flow discrete fracture matrix model

Jérôme Droniou, Julian Hennicker and Roland Masson
Numerische Mathematik 141 (1) 21 (2019)
https://doi.org/10.1007/s00211-018-0994-y

An Enriched Approach for Modeling Multiscale Discrete-Fracture/Matrix Interaction for Unconventional-Reservoir Simulations

Yang Xia, Yan Jin, Mian Chen and Kang Ping Chen
SPE Journal 24 (01) 349 (2019)
https://doi.org/10.2118/194012-PA

A multiscale flux basis for mortar mixed discretizations of reduced Darcy–Forchheimer fracture models

Elyes Ahmed, Alessio Fumagalli and Ana Budiša
Computer Methods in Applied Mechanics and Engineering 354 16 (2019)
https://doi.org/10.1016/j.cma.2019.05.034

Nonlocal multicontinuum (NLMC) upscaling of mixed dimensional coupled flow problem for embedded and discrete fracture models

Maria Vasilyeva, Eric T. Chung, Wing Tat Leung and Valentin Alekseev
GEM - International Journal on Geomathematics 10 (1) (2019)
https://doi.org/10.1007/s13137-019-0136-4

Flow and transport in fractured poroelastic media

Ilona Ambartsumyan, Eldar Khattatov, Truong Nguyen and Ivan Yotov
GEM - International Journal on Geomathematics 10 (1) (2019)
https://doi.org/10.1007/s13137-019-0119-5

Numerical Mathematics and Advanced Applications ENUMATH 2017

Eirik Keilegavlen, Alessio Fumagalli, Runar Berge and Ivar Stefansson
Lecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications ENUMATH 2017 126 573 (2019)
https://doi.org/10.1007/978-3-319-96415-7_52

A simple finite element method for elliptic bulk problems with embedded surfaces

Erik Burman, Peter Hansbo and Mats G. Larson
Computational Geosciences 23 (1) 189 (2019)
https://doi.org/10.1007/s10596-018-9792-y

Conforming, non-conforming and non-matching discretization couplings in discrete fracture network simulations

Alessio Fumagalli, Eirik Keilegavlen and Stefano Scialò
Journal of Computational Physics 376 694 (2019)
https://doi.org/10.1016/j.jcp.2018.09.048

Upscaling of the single-phase flow and heat transport in fractured geothermal reservoirs using nonlocal multicontinuum method

Maria Vasilyeva, Masoud Babaei, Eric T. Chung and Valentin Alekseev
Computational Geosciences 23 (4) 745 (2019)
https://doi.org/10.1007/s10596-019-9817-1

A Lagrange multiplier method for a discrete fracture model for flow in porous media

Markus Köppel, Vincent Martin, Jérôme Jaffré and Jean E. Roberts
Computational Geosciences 23 (2) 239 (2019)
https://doi.org/10.1007/s10596-018-9779-8

Constrained energy minimization based upscaling for coupled flow and mechanics

Maria Vasilyeva, Eric T. Chung, Yalchin Efendiev and Jihoon Kim
Journal of Computational Physics 376 660 (2019)
https://doi.org/10.1016/j.jcp.2018.09.054

A cut finite element method for elliptic bulk problems with embedded surfaces

Erik Burman, Peter Hansbo, Mats G. Larson and David Samvin
GEM - International Journal on Geomathematics 10 (1) (2019)
https://doi.org/10.1007/s13137-019-0120-z

A Hybrid High-Order method for passive transport in fractured porous media

Florent Chave, Daniele A. Di Pietro and Luca Formaggia
GEM - International Journal on Geomathematics 10 (1) (2019)
https://doi.org/10.1007/s13137-019-0114-x

A stabilized cut discontinuous Galerkin framework for elliptic boundary value and interface problems

Ceren Gürkan and André Massing
Computer Methods in Applied Mechanics and Engineering 348 466 (2019)
https://doi.org/10.1016/j.cma.2018.12.041

Discontinuous Galerkin Approximation of Flows in Fractured Porous Media on Polytopic Grids

Paola F. Antonietti, Chiara Facciolà, Alessandro Russo and Marco Verani
SIAM Journal on Scientific Computing 41 (1) A109 (2019)
https://doi.org/10.1137/17M1138194

Dual Virtual Element Methods for Discrete Fracture Matrix models

Alessio Fumagalli, Eirik Keilegavlen, A. Anciaux-Sedrakian and Q. H. Tran
Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 74 41 (2019)
https://doi.org/10.2516/ogst/2019008

Mixed-Dimensional Geometric Multigrid Methods for Single-Phase Flow in Fractured Porous Media

Andrés Arrarás, Francisco J. Gaspar, Laura Portero and Carmen Rodrigo
SIAM Journal on Scientific Computing 41 (5) B1082 (2019)
https://doi.org/10.1137/18M1224751

Nonlocal multicontinua upscaling for multicontinua flow problems in fractured porous media

Maria Vasilyeva, Eric T. Chung, Siu Wun Cheung, Yating Wang and Georgy Prokopev
Journal of Computational and Applied Mathematics 355 258 (2019)
https://doi.org/10.1016/j.cam.2019.01.024

Geometric multigrid methods for Darcy–Forchheimer flow in fractured porous media

A. Arrarás, F.J. Gaspar, L. Portero and C. Rodrigo
Computers & Mathematics with Applications 78 (9) 3139 (2019)
https://doi.org/10.1016/j.camwa.2019.04.031