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Multiscale VEM for the Biot consolidation analysis of complex and highly heterogeneous domains
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Forward modelling of geophysical electromagnetic data on unstructured grids using an adaptive mimetic finite-difference method
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) https://doi.org/10.1002/nme.6287
Mixed virtual element methods for elastodynamics with weak symmetry
A low-order nonconforming method for linear elasticity on general meshes
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Virtual element method for two-dimensional linear elasticity problem in mixed weakly symmetric formulation
Finite volume methods for elasticity with weak symmetry
Eirik Keilegavlen and Jan Martin Nordbotten International Journal for Numerical Methods in Engineering 112(8) 939 (2017) https://doi.org/10.1002/nme.5538
Mimetic finite difference methods for Hamiltonian wave equations in 2D
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) https://doi.org/10.1051/m2an/2015088
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) https://doi.org/10.1007/978-3-319-41640-3_10
Post processing of solution and flux for the nodal mimetic finite difference method
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Mimetic finite difference approximation of quasilinear elliptic problems
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A two-level method for mimetic finite difference discretizations of elliptic problems
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) https://doi.org/10.1142/S021820251440003X
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) https://doi.org/10.1142/S0218202514400016
New perspectives on polygonal and polyhedral finite element methods
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M-Adaptation in the mimetic finite difference method
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A displacement‐based finite element formulation for general polyhedra using harmonic shape functions
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) https://doi.org/10.1137/120873157
Numerical results for mimetic discretization of Reissner–Mindlin plate problems
L. BEIRÃO DA VEIGA, F. BREZZI, A. CANGIANI, G. MANZINI, L. D. MARINI and A. RUSSO Mathematical Models and Methods in Applied Sciences 23(01) 199 (2013) https://doi.org/10.1142/S0218202512500492
Virtual Elements for Linear Elasticity Problems
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A mimetic discretization of the Reissner–Mindlin plate bending problem