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Lipnikov, Konstantin
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A family of mimetic finite difference methods on polygonal and polyhedral meshes
F Brezzi, K Lipnikov, V Simoncini
Mathematical Models and Methods in Applied Sciences 15 (10), 1533-1551, 2005
4632005
Mimetic finite difference method
K Lipnikov, G Manzini, M Shashkov
Journal of Computational Physics 257, 1163-1227, 2014
4532014
Convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes
F Brezzi, K Lipnikov, M Shashkov
SIAM Journal on Numerical Analysis 43 (5), 1872-1896, 2005
4522005
The mimetic finite difference method for elliptic problems
LB da Veiga, K Lipnikov, G Manzini
Springer, 2014
3152014
Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes
K Lipnikov, M Shashkov, D Svyatskiy, Y Vassilevski
Journal of Computational Physics 227 (1), 492-512, 2007
2892007
Mimetic finite differences for elliptic problems
F Brezzi, A Buffa, K Lipnikov
ESAIM: Mathematical Modelling and Numerical Analysis 43 (2), 277-295, 2009
2402009
The nonconforming virtual element method
BA de Dios, K Lipnikov, G Manzini
ESAIM: Mathematical Modelling and Numerical Analysis 50 (3), 879-904, 2016
2312016
Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes
K Lipnikov, D Svyatskiy, Y Vassilevski
Journal of Computational Physics 228 (3), 703-716, 2009
1872009
A new discretization methodology for diffusion problems on generalized polyhedral meshes
F Brezzi, K Lipnikov, M Shashkov, V Simoncini
Computer Methods in Applied Mechanics and Engineering 196 (37-40), 3682-3692, 2007
1852007
Local flux mimetic finite difference methods
K Lipnikov, M Shashkov, I Yotov
Numerische Mathematik 112 (1), 115-152, 2009
1532009
Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes
K Lipnikov, J Morel, M Shashkov
Journal of Computational Physics 199 (2), 589-597, 2004
1482004
The mimetic finite difference method on polygonal meshes for diffusion-type problems
Y Kuznetsov, K Lipnikov, M Shashkov
Computational Geosciences 8 (4), 301-324, 2004
1362004
Arbitrary-order nodal mimetic discretizations of elliptic problems on polygonal meshes
LB Da Veiga, K Lipnikov, G Manzini
SIAM Journal on Numerical Analysis 49 (5), 1737-1760, 2011
1282011
Mimetic finite difference method for the Stokes problem on polygonal meshes
LB Da Veiga, V Gyrya, K Lipnikov, G Manzini
Journal of computational physics 228 (19), 7215-7232, 2009
1272009
Convergence of mimetic finite difference method for diffusion problems on polyhedral meshes with curved faces
F Brezzi, K Lipnikov, M Shashkov
Mathematical Models and Methods in Applied Sciences 16 (02), 275-297, 2006
1252006
The mimetic finite difference discretization of diffusion problem on unstructured polyhedral meshes
K Lipnikov, M Shashkov, D Svyatskiy
Journal of Computational Physics 211 (2), 473-491, 2006
1252006
A monotone finite volume method for advection–diffusion equations on unstructured polygonal meshes
K Lipnikov, D Svyatskiy, Y Vassilevski
Journal of Computational Physics 229 (11), 4017-4032, 2010
1042010
Analysis of the monotonicity conditions in the mimetic finite difference method for elliptic problems
K Lipnikov, G Manzini, D Svyatskiy
Journal of Computational Physics 230 (7), 2620-2642, 2011
872011
High-order mimetic finite difference method for diffusion problems on polygonal meshes
V Gyrya, K Lipnikov
Journal of Computational Physics 227 (20), 8841-8854, 2008
872008
Convergence analysis of the high-order mimetic finite difference method
L Beirão da Veiga, K Lipnikov, G Manzini
Numerische Mathematik 113 (3), 325-356, 2009
852009
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