hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes
ESAIM: M2AN, 50 3 (2016) 699-725
Published online: 2016-05-23
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:
This article has been cited by the following article(s):
Discontinuous Galerkin discretization of coupled poroelasticity–elasticity problems
Paola F Antonietti, Michele Botti and Ilario MazzieriIMA Journal of Numerical Analysis 45 (6) 3438 (2025)
https://doi.org/10.1093/imanum/drae093
https://doi.org/10.1016/bs.aams.2025.08.004
Level-Set Shape Optimization via Polytopic Discontinuous Galerkin Methods
Raphael S. Fernandes, Emmanuil H. Georgoulis and Alberto PaganiniSIAM Journal on Scientific Computing 47 (5) B1293 (2025)
https://doi.org/10.1137/24M1687595
Numerical Model for 1D–2D Pollutant Transport Problems
Ingrid L. Simanungkalit and Ikha MagdalenaJournal of Physics: Conference Series 3114 (1) 012007 (2025)
https://doi.org/10.1088/1742-6596/3114/1/012007
A p-adaptive polytopal discontinuous Galerkin method for high-order approximation of brain electrophysiology
Caterina B․ Leimer Saglio, Stefano Pagani and Paola F․ AntoniettiComputer Methods in Applied Mechanics and Engineering 446 118249 (2025)
https://doi.org/10.1016/j.cma.2025.118249
lymph : Discontinuous Polytopal Methods for Multi-Physics Differential Problems
Paola F. Antonietti, Stefano Bonetti, Michele Botti, Mattia Corti, Ivan Fumagalli and Ilario MazzieriACM Transactions on Mathematical Software 51 (1) 1 (2025)
https://doi.org/10.1145/3716310
A polytopal discontinuous Galerkin method for the pseudo-stress formulation of the unsteady Stokes problem
Paola F. Antonietti, Michele Botti, Alessandra Cancrini and Ilario MazzieriComputer Methods in Applied Mechanics and Engineering 447 118404 (2025)
https://doi.org/10.1016/j.cma.2025.118404
Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport
Paul Houston, Matthew E. Hubbard, Thomas J. Radley, Oliver J. Sutton and Richard S. J. WiddowsonJournal of Scientific Computing 100 (2) (2024)
https://doi.org/10.1007/s10915-024-02569-3
Adaptive discontinuous Galerkin finite element methods for the Allen-Cahn equation on polygonal meshes
Rui Li, Yali Gao and Zhangxin ChenNumerical Algorithms 95 (4) 1981 (2024)
https://doi.org/10.1007/s11075-023-01635-5
The eXtended virtual element method for elliptic problems with weakly singular solutions
Jérôme Droniou, Gianmarco Manzini and Liam YemmComputer Methods in Applied Mechanics and Engineering 429 117129 (2024)
https://doi.org/10.1016/j.cma.2024.117129
Error estimates for completely discrete FEM in energy‐type and weaker norms
Lutz Angermann, Peter Knabner and Andreas RuppNumerical Methods for Partial Differential Equations 40 (6) (2024)
https://doi.org/10.1002/num.23106
Discontinuous Galerkin methods for Fisher–Kolmogorov equation with application to α-synuclein spreading in Parkinson’s disease
Mattia Corti, Francesca Bonizzoni, Luca Dede’, Alfio M. Quarteroni and Paola F. AntoniettiComputer Methods in Applied Mechanics and Engineering 417 116450 (2023)
https://doi.org/10.1016/j.cma.2023.116450
A High-Order Discontinuous Galerkin Method for the Poro-elasto-acoustic Problem on Polygonal and Polyhedral Grids
Paola F. Antonietti, Michele Botti, Ilario Mazzieri and Simone Nati PoltriSIAM Journal on Scientific Computing 44 (1) B1 (2022)
https://doi.org/10.1137/21M1410919
On Mathematical and Numerical Modelling of Multiphysics Wave Propagation with Polytopal Discontinuous Galerkin Methods: a Review
Paola F. Antonietti, Michele Botti and Ilario MazzieriVietnam Journal of Mathematics 50 (4) 997 (2022)
https://doi.org/10.1007/s10013-022-00566-3
Stability Analysis of Polytopic Discontinuous Galerkin Approximations of the Stokes Problem with Applications to Fluid–Structure Interaction Problems
Paola F. Antonietti, Lorenzo Mascotto, Marco Verani and Stefano ZoncaJournal of Scientific Computing 90 (1) (2022)
https://doi.org/10.1007/s10915-021-01695-6
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 VeraniComputers & Mathematics with Applications 116 116 (2022)
https://doi.org/10.1016/j.camwa.2021.08.015
Robust Interior Penalty Discontinuous Galerkin Methods
Zhaonan Dong and Emmanuil H. GeorgoulisJournal of Scientific Computing 92 (2) (2022)
https://doi.org/10.1007/s10915-022-01916-6
ℎ𝑝-version discontinuous Galerkin methods on essentially arbitrarily-shaped elements
Andrea Cangiani, Zhaonan Dong and Emmanuil GeorgoulisMathematics of Computation 91 (333) 1 (2021)
https://doi.org/10.1090/mcom/3667
SUPG-stabilized virtual elements for diffusion-convection problems: a robustness analysis
Lourenco Beirão da Veiga, Franco Dassi, Carlo Lovadina and Giuseppe VaccaESAIM: Mathematical Modelling and Numerical Analysis 55 (5) 2233 (2021)
https://doi.org/10.1051/m2an/2021050
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
GPU-Accelerated Discontinuous Galerkin Methods on Polytopic Meshes
Zhaonan Dong, Emmanuil H. Georgoulis and Thomas KappasSIAM Journal on Scientific Computing 43 (4) C312 (2021)
https://doi.org/10.1137/20M1350984
An efficient parallel scheme based on the nodal discontinuous Galerkin method for fluid flow simulations
Amjad Ali, Muhammad Umar, Hamayun Farooq and Muhammad IshaqAIP Advances 11 (6) (2021)
https://doi.org/10.1063/5.0054784
A discontinuous Galerkin method by patch reconstruction for convection-diffusion-reaction problems over polytopic meshes
Di Yang and Yinnian HeComputers & Mathematics with Applications 97 175 (2021)
https://doi.org/10.1016/j.camwa.2021.05.035
A high-order discontinuous Galerkin method for nonlinear sound waves
Paola F. Antonietti, Ilario Mazzieri, Markus Muhr, Vanja Nikolić and Barbara WohlmuthJournal of Computational Physics 415 109484 (2020)
https://doi.org/10.1016/j.jcp.2020.109484
A space-time discontinuous Galerkin method for the elastic wave equation
Paola F. Antonietti, Ilario Mazzieri and Francesco MiglioriniJournal of Computational Physics 419 109685 (2020)
https://doi.org/10.1016/j.jcp.2020.109685
A high-order discontinuous Galerkin approach to the elasto-acoustic problem
Paola F. Antonietti, Francesco Bonaldi and Ilario MazzieriComputer Methods in Applied Mechanics and Engineering 358 112634 (2020)
https://doi.org/10.1016/j.cma.2019.112634
A painless automatic hp-adaptive strategy for elliptic problems
Vincent Darrigrand, David Pardo, Théophile Chaumont-Frelet, Ignacio Gómez-Revuelto and Luis Emilio Garcia-CastilloFinite Elements in Analysis and Design 178 103424 (2020)
https://doi.org/10.1016/j.finel.2020.103424
The conforming virtual element method for polyharmonic problems
P.F. Antonietti, G. Manzini and M. VeraniComputers & Mathematics with Applications 79 (7) 2021 (2020)
https://doi.org/10.1016/j.camwa.2019.09.022
Unified analysis of discontinuous Galerkin approximations of flows in fractured porous media on polygonal and polyhedral grids
Paola F. Antonietti, Chiara Facciolà and Marco VeraniMathematics in Engineering 2 (2) 340 (2020)
https://doi.org/10.3934/mine.2020017
Recovered finite element methods on polygonal and polyhedral meshes
Zhaonan Dong, Emmanuil H. Georgoulis and Tristan PryerESAIM: Mathematical Modelling and Numerical Analysis 54 (4) 1309 (2020)
https://doi.org/10.1051/m2an/2019047
An Arbitrary-Order Discontinuous Galerkin Method with One Unknown Per Element
Ruo Li, Pingbing Ming, Ziyuan Sun and Zhijian YangJournal of Scientific Computing 80 (1) 268 (2019)
https://doi.org/10.1007/s10915-019-00937-y
Discontinuous Galerkin Approximation of Flows in Fractured Porous Media on Polytopic Grids
Paola F. Antonietti, Chiara Facciolà, Alessandro Russo and Marco VeraniSIAM Journal on Scientific Computing 41 (1) A109 (2019)
https://doi.org/10.1137/17M1138194
V-cycle Multigrid Algorithms for Discontinuous Galerkin Methods on Non-nested Polytopic Meshes
P. F. Antonietti and G. PennesiJournal of Scientific Computing 78 (1) 625 (2019)
https://doi.org/10.1007/s10915-018-0783-x
On the exponent of exponential convergence of p-version FEM spaces
Zhaonan DongAdvances in Computational Mathematics 45 (2) 757 (2019)
https://doi.org/10.1007/s10444-018-9637-1
High-order Discontinuous Galerkin methods for the elastodynamics equation on polygonal and polyhedral meshes
P.F. Antonietti and I. MazzieriComputer Methods in Applied Mechanics and Engineering 342 414 (2018)
https://doi.org/10.1016/j.cma.2018.08.012
A multigrid algorithm for the p-version of the virtual element method
Paola F. Antonietti, Lorenzo Mascotto and Marco VeraniESAIM: Mathematical Modelling and Numerical Analysis 52 (1) 337 (2018)
https://doi.org/10.1051/m2an/2018007
Non-conforming Harmonic Virtual Element Method: $$h$$ h - and $$p$$ p -Versions
Lorenzo Mascotto, Ilaria Perugia and Alexander PichlerJournal of Scientific Computing 77 (3) 1874 (2018)
https://doi.org/10.1007/s10915-018-0797-4
Fast Numerical Integration on Polytopic Meshes with Applications to Discontinuous Galerkin Finite Element Methods
Paola F. Antonietti, Paul Houston and Giorgio PennesiJournal of Scientific Computing 77 (3) 1339 (2018)
https://doi.org/10.1007/s10915-018-0802-y
Recovered finite element methods
Emmanuil H. Georgoulis and Tristan PryerComputer Methods in Applied Mechanics and Engineering 332 303 (2018)
https://doi.org/10.1016/j.cma.2017.12.026
A Brief Review on Polygonal/Polyhedral Finite Element Methods
Logah PerumalMathematical Problems in Engineering 2018 1 (2018)
https://doi.org/10.1155/2018/5792372
Hexagonal Smoothness-Increasing Accuracy-Conserving Filtering
Mahsa Mirzargar, Ashok Jallepalli, Jennifer K. Ryan and Robert M. KirbyJournal of Scientific Computing 73 (2-3) 1072 (2017)
https://doi.org/10.1007/s10915-017-0517-5
A Discontinuous Galerkin Method for the Wave Equation: A hp-a Priori Error Estimate
Abdelhamid Zaghdani, M. Ezzat Mohamed and A.I. El-MaghrabJournal of Applied Sciences 17 (2) 81 (2017)
https://doi.org/10.3923/jas.2017.81.89
Multigrid algorithms for $$\varvec{hp}$$ h p -version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes
P. F. Antonietti, P. Houston, X. Hu, M. Sarti and M. VeraniCalcolo 54 (4) 1169 (2017)
https://doi.org/10.1007/s10092-017-0223-6
hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes
Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis and Paul HoustonSpringerBriefs in Mathematics, hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes 87 (2017)
https://doi.org/10.1007/978-3-319-67673-9_6
A posteriori error estimates for the virtual element method
Andrea Cangiani, Emmanuil H. Georgoulis, Tristan Pryer and Oliver J. SuttonNumerische Mathematik 137 (4) 857 (2017)
https://doi.org/10.1007/s00211-017-0891-9
h-multigrid agglomeration based solution strategies for discontinuous Galerkin discretizations of incompressible flow problems
L. Botti, A. Colombo and F. BassiJournal of Computational Physics 347 382 (2017)
https://doi.org/10.1016/j.jcp.2017.07.002
hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes
Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis and Paul HoustonSpringerBriefs in Mathematics, hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes 23 (2017)
https://doi.org/10.1007/978-3-319-67673-9_3
$hp$-Version Space-Time Discontinuous Galerkin Methods for Parabolic Problems on Prismatic Meshes
Andrea Cangiani, Zhaonan Dong and Emmanuil H. GeorgoulisSIAM Journal on Scientific Computing 39 (4) A1251 (2017)
https://doi.org/10.1137/16M1073285
Advances in Discretization Methods
Joe Collis and Paul HoustonSEMA SIMAI Springer Series, Advances in Discretization Methods 12 187 (2016)
https://doi.org/10.1007/978-3-319-41246-7_9
Preface
L. Beirão da Veiga and A. ErnESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 633 (2016)
https://doi.org/10.1051/m2an/2016034
Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations
Paola F. Antonietti, Andrea Cangiani, Joe Collis, et al.Lecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 281 (2016)
https://doi.org/10.1007/978-3-319-41640-3_9