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):

A high-order mimetic method on unstructured polyhedral meshes for the diffusion equation

K. Lipnikov and G. Manzini
Journal of Computational Physics 272 360 (2014)
DOI: 10.1016/j.jcp.2014.04.021
See this article

Mimetic scalar products of discrete differential forms

F. Brezzi, A. Buffa and G. Manzini
Journal of Computational Physics 257 1228 (2014)
DOI: 10.1016/j.jcp.2013.08.017
See this article

A two-level method for mimetic finite difference discretizations of elliptic problems

Paola F. Antonietti, Marco Verani and Ludmil Zikatanov
Computers & Mathematics with Applications 70 (11) 2674 (2015)
DOI: 10.1016/j.camwa.2015.06.010
See this article

Virtual Elements for Linear Elasticity Problems

L. Beira͂o da Veiga, F. Brezzi and L. D. Marini
SIAM Journal on Numerical Analysis 51 (2) 794 (2013)
DOI: 10.1137/120874746
See this article

Topology optimization using polytopes

Arun L. Gain, Glaucio H. Paulino, Leonardo S. Duarte and Ivan F.M. Menezes
Computer Methods in Applied Mechanics and Engineering 293 411 (2015)
DOI: 10.1016/j.cma.2015.05.007
See this article

Mimetic Discretizations of Elliptic Control Problems

Paola F. Antonietti, Nadia Bigoni and Marco Verani
Journal of Scientific Computing 56 (1) 14 (2013)
DOI: 10.1007/s10915-012-9659-7
See this article

Numerical results for mimetic discretization of Reissner–Mindlin plate problems

Lourenço Beirão da Veiga, Carlo Lovadina and David Mora
Calcolo 50 (3) 209 (2013)
DOI: 10.1007/s10092-012-0065-1
See this article

Hierarchical A Posteriori Error Estimators for the Mimetic Discretization of Elliptic Problems

Paola F. Antonietti, Lourenco Beira͂o da Veiga, Carlo Lovadina and Marco Verani
SIAM Journal on Numerical Analysis 51 (1) 654 (2013)
DOI: 10.1137/120873157
See this article

Mimetic finite difference approximation of quasilinear elliptic problems

Paola F. Antonietti, Nadia Bigoni and Marco Verani
Calcolo 52 (1) 45 (2015)
DOI: 10.1007/s10092-014-0107-y
See this article

Error Analysis for a Mimetic Discretization of the Steady Stokes Problem on Polyhedral Meshes

L. Beirão da Veiga, K. Lipnikov and G. Manzini
SIAM Journal on Numerical Analysis 48 (4) 1419 (2010)
DOI: 10.1137/090757411
See this article

New perspectives on polygonal and polyhedral finite element methods

Gianmarco Manzini, Alessandro Russo and N. Sukumar
Mathematical Models and Methods in Applied Sciences 24 (08) 1665 (2014)
DOI: 10.1142/S0218202514400065
See this article

Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

Konstantin Lipnikov and Gianmarco Manzini
Lecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 311 (2016)
DOI: 10.1007/978-3-319-41640-3_10
See this article

Analysis of the monotonicity conditions in the mimetic finite difference method for elliptic problems

K. Lipnikov, G. Manzini and D. Svyatskiy
Journal of Computational Physics 230 (7) 2620 (2011)
DOI: 10.1016/j.jcp.2010.12.039
See this article

On the Virtual Element Method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes

Arun L. Gain, Cameron Talischi and Glaucio H. Paulino
Computer Methods in Applied Mechanics and Engineering 282 132 (2014)
DOI: 10.1016/j.cma.2014.05.005
See this article

Spectral properties and conservation laws in Mimetic Finite Difference methods for PDEs

Luciano Lopez and Giuseppe Vacca
Journal of Computational and Applied Mathematics 292 760 (2016)
DOI: 10.1016/j.cam.2015.01.024
See this article

M-Adaptation in the mimetic finite difference method

Vitaliy Gyrya, Konstantin Lipnikov, Gianmarco Manzini and Daniil Svyatskiy
Mathematical Models and Methods in Applied Sciences 24 (08) 1621 (2014)
DOI: 10.1142/S0218202514400053
See this article

Finite volume methods for elasticity with weak symmetry

Eirik Keilegavlen and Jan Martin Nordbotten
International Journal for Numerical Methods in Engineering (2017)
DOI: 10.1002/nme.5538
See this article

Arbitrary-Order Nodal Mimetic Discretizations of Elliptic Problems on Polygonal Meshes

L. Beirão da Veiga, K. Lipnikov and G. Manzini
SIAM Journal on Numerical Analysis 49 (5) 1737 (2011)
DOI: 10.1137/100807764
See this article

A hybrid high-order locking-free method for linear elasticity on general meshes

Daniele A. Di Pietro and Alexandre Ern
Computer Methods in Applied Mechanics and Engineering 283 1 (2015)
DOI: 10.1016/j.cma.2014.09.009
See this article

Mimetic finite differences for nonlinear and control problems

P. F. Antonietti, L. Beirão da Veiga, N. Bigoni and M. Verani
Mathematical Models and Methods in Applied Sciences 24 (08) 1457 (2014)
DOI: 10.1142/S0218202514400016
See this article

Mimetic finite difference methods for Hamiltonian wave equations in 2D

L. Beirão da Veiga, L. Lopez and G. Vacca
Computers & Mathematics with Applications (2017)
DOI: 10.1016/j.camwa.2017.05.022
See this article

Equivalent projectors for virtual element methods

B. Ahmad, A. Alsaedi, F. Brezzi, L.D. Marini and A. Russo
Computers & Mathematics with Applications 66 (3) 376 (2013)
DOI: 10.1016/j.camwa.2013.05.015
See this article

The Hitchhiker's Guide to the Virtual Element Method

L. Beirão da Veiga, F. Brezzi, L. D. Marini and A. Russo
Mathematical Models and Methods in Applied Sciences 24 (08) 1541 (2014)
DOI: 10.1142/S021820251440003X
See this article

A displacement-based finite element formulation for general polyhedra using harmonic shape functions

J.E. Bishop
International Journal for Numerical Methods in Engineering 97 (1) 1 (2014)
DOI: 10.1002/nme.4562
See this article

Mimetic finite difference method

Konstantin Lipnikov, Gianmarco Manzini and Mikhail Shashkov
Journal of Computational Physics 257 1163 (2014)
DOI: 10.1016/j.jcp.2013.07.031
See this article

A mimetic discretization of the Reissner–Mindlin plate bending problem

L. Beirão da Veiga and D. Mora
Numerische Mathematik 117 (3) 425 (2011)
DOI: 10.1007/s00211-010-0358-8
See this article

Post processing of solution and flux for the nodal mimetic finite difference method

Lourenço Beirão da Veiga, Gianmarco Manzini and Mario Putti
Numerical Methods for Partial Differential Equations 31 (1) 336 (2015)
DOI: 10.1002/num.21907
See this article

The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes

K. Lipnikov, G. Manzini, F. Brezzi and A. Buffa
Journal of Computational Physics 230 (2) 305 (2011)
DOI: 10.1016/j.jcp.2010.09.007
See this article

BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS

L. BEIRÃO DA VEIGA, F. BREZZI, A. CANGIANI, et al.
Mathematical Models and Methods in Applied Sciences 23 (01) 199 (2013)
DOI: 10.1142/S0218202512500492
See this article

The arbitrary order mixed mimetic finite difference method for the diffusion equation

Vitaliy Gyrya, Konstantin Lipnikov and Gianmarco Manzini
ESAIM: Mathematical Modelling and Numerical Analysis 50 (3) 851 (2016)
DOI: 10.1051/m2an/2015088
See this article

Mixed virtual element methods for elastodynamics with weak symmetry

Baiju Zhang, Yan Yang and Minfu Feng
Journal of Computational and Applied Mathematics 353 49 (2019)
DOI: 10.1016/j.cam.2018.12.020
See this article

A multipoint stress mixed finite element method for elasticity on quadrilateral grids

Ilona Ambartsumyan, Eldar Khattatov, Jan Martin Nordbotten and Ivan Yotov
Numerical Methods for Partial Differential Equations 37 (3) 1886 (2021)
DOI: 10.1002/num.22624
See this article

A low-order nonconforming method for linear elasticity on general meshes

Michele Botti, Daniele A. Di Pietro and Alessandra Guglielmana
Computer Methods in Applied Mechanics and Engineering 354 96 (2019)
DOI: 10.1016/j.cma.2019.05.031
See this article

Cell-centered finite-volume method for elastic deformation of heterogeneous media with full-tensor properties

Kirill M. Terekhov and Hamdi A. Tchelepi
Journal of Computational and Applied Mathematics 364 112331 (2020)
DOI: 10.1016/j.cam.2019.06.047
See this article

Forward modelling of geophysical electromagnetic data on unstructured grids using an adaptive mimetic finite-difference method

Hormoz Jahandari and Alex Bihlo
Computational Geosciences (2021)
DOI: 10.1007/s10596-021-10042-5
See this article

An enhanced octree polyhedral scaled boundary finite element method and its applications in structure analysis

Degao Zou, Kai Chen, Xianjing Kong and Jingmao Liu
Engineering Analysis with Boundary Elements 84 87 (2017)
DOI: 10.1016/j.enganabound.2017.07.007
See this article

An enhanced VEM formulation for plane elasticity

A.M. D’Altri, S. de Miranda, L. Patruno and E. Sacco
Computer Methods in Applied Mechanics and Engineering 376 113663 (2021)
DOI: 10.1016/j.cma.2020.113663
See this article

Virtual element method for two-dimensional linear elasticity problem in mixed weakly symmetric formulation

Baiju Zhang and Minfu Feng
Applied Mathematics and Computation 328 1 (2018)
DOI: 10.1016/j.amc.2018.01.023
See this article

A multiscale virtual element method for the analysis of heterogeneous media

Abhilash Sreekumar, Savvas P. Triantafyllou, François‐Xavier Bécot and Fabien Chevillotte
International Journal for Numerical Methods in Engineering 121 (8) 1791 (2020)
DOI: 10.1002/nme.6287
See this article

L. Beirão da Veiga and G. Manzini
2616 (2014)
DOI: 10.5151/meceng-wccm2012-18943
See this article

Multiscale VEM for the Biot consolidation analysis of complex and highly heterogeneous domains

Abhilash Sreekumar, Savvas P. Triantafyllou, François-Xavier Bécot and Fabien Chevillotte
Computer Methods in Applied Mechanics and Engineering 375 113543 (2021)
DOI: 10.1016/j.cma.2020.113543
See this article

A low-order finite element method for three dimensional linear elasticity problems with general meshes

Thi-Thao-Phuong Hoang, Duc Cam Hai Vo and Thanh Hai Ong
Computers & Mathematics with Applications 74 (6) 1379 (2017)
DOI: 10.1016/j.camwa.2017.06.023
See this article