Annotations on the virtual element method for second-order elliptic problems
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[1] Raytcho D. Lazarov,et al. Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems , 2009, SIAM J. Numer. Anal..
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[30] Gianmarco Manzini,et al. Virtual Element Methods for Elliptic Problems on Polygonal Meshes , 2017 .
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[32] Gianmarco Manzini,et al. Discretization of Mixed Formulations of Elliptic Problems on Polyhedral Meshes , 2016, 1610.05850.
[33] Stefano Berrone,et al. A hybrid mortar virtual element method for discrete fracture network simulations , 2016, J. Comput. Phys..
[34] L. Beirao da Veiga,et al. Serendipity Nodal VEM spaces , 2015, 1510.08477.
[35] R. Eymard,et al. A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS , 2008, 0812.2097.
[36] Gianmarco Manzini,et al. M-Adaptation in the mimetic finite difference method , 2014 .
[37] Gianmarco Manzini,et al. Convergence Analysis of the Mimetic Finite Difference Method for Elliptic Problems , 2009, SIAM J. Numer. Anal..
[38] Haiying Wang,et al. Superconvergent discontinuous Galerkin methods for second-order elliptic problems , 2009, Math. Comput..
[39] Marc I. Gerritsma,et al. A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations , 2016, J. Comput. Phys..
[40] Shaochun Chen,et al. The nonconforming virtual element method for plate bending problems , 2016 .
[41] Simone Scacchi,et al. A C1 Virtual Element Method for the Cahn-Hilliard Equation with Polygonal Meshes , 2015, SIAM J. Numer. Anal..
[42] Markus H. Gross,et al. Polyhedral Finite Elements Using Harmonic Basis Functions , 2008, Comput. Graph. Forum.
[43] Gian Luca Delzanno,et al. A Legendre-Fourier spectral method with exact conservation laws for the Vlasov-Poisson system , 2016, J. Comput. Phys..
[44] Franco Brezzi,et al. The Hitchhiker's Guide to the Virtual Element Method , 2014 .
[45] Gianmarco Manzini,et al. A Higher-Order Formulation of the Mimetic Finite Difference Method , 2008, SIAM J. Sci. Comput..
[46] Gianmarco Manzini,et al. Convergence analysis of the high-order mimetic finite difference method , 2009, Numerische Mathematik.
[47] M. Shashkov,et al. A new discretization methodology for diffusion problems on generalized polyhedral meshes , 2007 .
[48] Junping Wang,et al. A computational study of the weak Galerkin method for second-order elliptic equations , 2011, Numerical Algorithms.
[49] I. Babuska,et al. Acta Numerica 2003: Survey of meshless and generalized finite element methods: A unified approach , 2003 .
[50] Gianmarco Manzini,et al. Conforming and nonconforming virtual element methods for elliptic problems , 2015, 1507.03543.
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[52] Glaucio H. Paulino,et al. On the Virtual Element Method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes , 2014 .
[53] T. Belytschko,et al. The extended/generalized finite element method: An overview of the method and its applications , 2010 .
[54] Paola F. Antonietti,et al. Mimetic finite differences for nonlinear and control problems , 2014 .
[55] Arun L. Gain. Polytope-based topology optimization using a mimetic-inspired method , 2014 .
[56] Chandrajit L. Bajaj,et al. Interpolation error estimates for mean value coordinates over convex polygons , 2011, Adv. Comput. Math..
[57] Ivo Babuška,et al. Generalized finite element methods for three-dimensional structural mechanics problems , 2000 .
[58] Gianmarco Manzini,et al. Residual a posteriori error estimation for the Virtual Element Method for elliptic problems , 2015 .
[59] Gianmarco Manzini,et al. Error Analysis for a Mimetic Discretization of the Steady Stokes Problem on Polyhedral Meshes , 2010, SIAM J. Numer. Anal..
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[61] F. Hermeline. Approximation of 2-D and 3-D diffusion operators with variable full tensor coefficients on arbitrary meshes , 2007 .
[62] A. Ern,et al. A Hybrid High-Order method for the incompressible Navier-Stokes equations based on Temam's device , 2018, J. Comput. Phys..
[63] Gianmarco Manzini,et al. Monotonicity Conditions in the Mimetic Finite Difference Method , 2011 .
[64] L. Beirao da Veiga,et al. Mixed Virtual Element Methods for general second order elliptic problems on polygonal meshes , 2014 .
[65] Kai Hormann,et al. A general construction of barycentric coordinates over convex polygons , 2006, Adv. Comput. Math..
[66] Gabriel N. Gatica,et al. A mixed virtual element method for the pseudostress–velocity formulation of the Stokes problem , 2017 .
[67] Francesca Gardini,et al. Virtual element method for second-order elliptic eigenvalue problems , 2016, 1610.03675.
[68] Glaucio H. Paulino,et al. Polygonal finite elements for topology optimization: A unifying paradigm , 2010 .
[69] L. Beirao da Veiga,et al. Basic principles of hp virtual elements on quasiuniform meshes , 2015, 1508.02242.
[70] Lourenço Beirão da Veiga,et al. Virtual Elements for Linear Elasticity Problems , 2013, SIAM J. Numer. Anal..
[71] Joseph E. Bishop,et al. A displacement‐based finite element formulation for general polyhedra using harmonic shape functions , 2014 .
[72] Ahmed Alsaedi,et al. Equivalent projectors for virtual element methods , 2013, Comput. Math. Appl..
[73] Alexandre Ern,et al. An Arbitrary-Order and Compact-Stencil Discretization of Diffusion on General Meshes Based on Local Reconstruction Operators , 2014, Comput. Methods Appl. Math..
[74] Alexandre Ern,et al. Hybrid high-order methods for variable-diffusion problems on general meshes , 2015 .
[75] Gianmarco Manzini,et al. Mimetic finite difference method , 2014, J. Comput. Phys..
[76] I. Babuska,et al. GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE , 2004 .
[77] Gianmarco Manzini,et al. Convergence of the mimetic finite difference method for eigenvalue problems in mixed form , 2011 .
[78] Eugenio Oñate,et al. The meshless finite element method , 2003 .
[79] T. Belytschko,et al. Extended finite element method for three-dimensional crack modelling , 2000 .
[80] Gianmarco Manzini,et al. Mimetic scalar products of discrete differential forms , 2014, J. Comput. Phys..
[81] K. Lipnikov,et al. The nonconforming virtual element method , 2014, 1405.3741.
[82] Joe D. Warren,et al. Barycentric coordinates for convex polytopes , 1996, Adv. Comput. Math..
[83] Pascal Omnes,et al. A FINITE VOLUME METHOD FOR THE LAPLACE EQUATION ON ALMOST ARBITRARY TWO-DIMENSIONAL GRIDS , 2005 .
[84] F. Hermeline,et al. A Finite Volume Method for the Approximation of Diffusion Operators on Distorted Meshes , 2000 .
[85] Gian Luca Delzanno,et al. Multi-dimensional, fully-implicit, spectral method for the Vlasov-Maxwell equations with exact conservation laws in discrete form , 2015, J. Comput. Phys..
[86] YE JUNPINGWANGANDXIU. A WEAK GALERKIN MIXED FINITE ELEMENT METHOD FOR SECOND ORDER ELLIPTIC PROBLEMS , 2014 .
[87] Gianmarco Manzini,et al. Convergence Analysis of the mimetic Finite Difference Method for Elliptic Problems with Staggered Discretizations of Diffusion Coefficients , 2016, SIAM J. Numer. Anal..
[88] Shan Zhao,et al. WEAK GALERKIN METHODS FOR SECOND ORDER ELLIPTIC INTERFACE PROBLEMS. , 2013, Journal of computational physics.
[89] Michael S. Floater,et al. Gradient Bounds for Wachspress Coordinates on Polytopes , 2013, SIAM J. Numer. Anal..
[90] Lourenço Beirão da Veiga,et al. Hierarchical A Posteriori Error Estimators for the Mimetic Discretization of Elliptic Problems , 2013, SIAM J. Numer. Anal..
[91] L. R. Scott,et al. The Mathematical Theory of Finite Element Methods , 1994 .
[92] Gianmarco Manzini,et al. Recent techniques for PDE discretizations on polyhedral meshes , 2014 .
[93] A. Ern,et al. Mathematical Aspects of Discontinuous Galerkin Methods , 2011 .
[94] Gianmarco Manzini,et al. The arbitrary order mixed mimetic finite difference method for the diffusion equation , 2016 .
[95] L. B. D. Veiga,et al. A virtual element method with arbitrary regularity , 2014 .
[96] L. Beirao da Veiga,et al. H(div) and H(curl)-conforming VEM , 2014, 1407.6822.
[97] Paola F. Antonietti,et al. Mimetic Discretizations of Elliptic Control Problems , 2013, J. Sci. Comput..
[98] Gianmarco Manzini,et al. Hourglass stabilization and the virtual element method , 2015 .
[99] Stefano Berrone,et al. A globally conforming method for solving flow in discrete fracture networks using the Virtual Element Method , 2016 .
[100] Annalisa Buffa,et al. Mimetic finite differences for elliptic problems , 2009 .
[101] Glaucio H. Paulino,et al. Some basic formulations of the virtual element method (VEM) for finite deformations , 2017 .
[102] A. Russo,et al. New perspectives on polygonal and polyhedral finite element methods , 2014 .
[103] Michael Ortiz,et al. Local Maximum-Entropy Approximation Schemes , 2007 .
[104] Gianmarco Manzini,et al. The Discrete Duality Finite Volume Method for Stokes Equations on Three-Dimensional Polyhedral Meshes , 2012, SIAM J. Numer. Anal..
[105] Gianmarco Manzini,et al. Flux reconstruction and solution post-processing in mimetic finite difference methods , 2008 .
[106] W. Wall,et al. An eXtended Finite Element Method/Lagrange multiplier based approach for fluid-structure interaction , 2008 .
[107] Paola F. Antonietti,et al. Mimetic finite difference approximation of quasilinear elliptic problems , 2015 .
[108] Eugene L. Wachspress,et al. Rational bases for convex polyhedra , 2010, Comput. Math. Appl..
[109] F. Hermeline,et al. Approximation of diffusion operators with discontinuous tensor coefficients on distorted meshes , 2003 .
[110] N. Sukumar,et al. Archives of Computational Methods in Engineering Recent Advances in the Construction of Polygonal Finite Element Interpolants , 2022 .
[111] Franco Brezzi,et al. Virtual Element Methods for plate bending problems , 2013 .
[112] Pavel B. Bochev,et al. Principles of Mimetic Discretizations of Differential Operators , 2006 .
[113] Alexandre Ern,et al. Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods , 2016 .
[114] Glaucio H. Paulino,et al. Topology optimization using polytopes , 2013, 1312.7016.
[115] Oliver J. Sutton,et al. The virtual element method in 50 lines of MATLAB , 2016, Numerical Algorithms.
[116] David Mora,et al. A posteriori error estimates for a Virtual Element Method for the Steklov eigenvalue problem , 2016, Comput. Math. Appl..
[117] Stefano Berrone,et al. Order preserving SUPG stabilization for the Virtual Element formulation of advection-diffusion problems , 2016 .
[118] Gian Luca Delzanno,et al. On the velocity space discretization for the Vlasov-Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods , 2016, Comput. Phys. Commun..
[119] Gianmarco Manzini,et al. A high-order mimetic method on unstructured polyhedral meshes for the diffusion equation , 2014, J. Comput. Phys..
[120] Erwin Laure,et al. Spectral Solver for Multi-scale Plasma Physics Simulations with Dynamically Adaptive Number of Moments , 2015, ICCS.
[121] Gianmarco Manzini,et al. A unified approach for handling convection terms in finite volumes and mimetic discretization methods for elliptic problems , 2011 .
[122] Richard S. Falk,et al. Basic principles of mixed Virtual Element Methods , 2014 .
[123] Stéphane Bordas,et al. Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods , 2015 .
[124] Peter Wriggers,et al. A virtual element method for contact , 2016 .
[125] Gianmarco Manzini,et al. Mimetic finite difference method for the Stokes problem on polygonal meshes , 2009, J. Comput. Phys..
[126] Gianmarco Manzini,et al. An a posteriori error estimator for the mimetic finite difference approximation of elliptic problems , 2008 .
[127] Gianmarco Manzini,et al. Analysis of the monotonicity conditions in the mimetic finite difference method for elliptic problems , 2011, J. Comput. Phys..
[128] Ilaria Perugia,et al. A Plane Wave Virtual Element Method for the Helmholtz Problem , 2015, 1505.04965.
[129] Odd Andersen,et al. On the use of the Virtual Element Method for geomechanics on reservoir grids , 2016 .