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
305 2007 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
202 2009 Integrated surface/subsurface permafrost thermal hydrology: Model formulation and proof‐of‐concept simulations SL Painter, ET Coon, AL Atchley, M Berndt, R Garimella, JD Moulton, ...
Water Resources Research 52 (8), 6062-6077, 2016
129 2016 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
128 2006 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
114 2010 A constrained finite element method satisfying the discrete maximum principle for anisotropic diffusion problems D Kuzmin, MJ Shashkov, D Svyatskiy
Journal of Computational Physics 228 (9), 3448-3463, 2009
97 2009 Verification benchmarks for single-phase flow in three-dimensional fractured porous media I Berre, WM Boon, B Flemisch, A Fumagalli, D Gläser, E Keilegavlen, ...
Advances in Water Resources 147, 103759, 2021
93 2021 Minimal stencil finite volume scheme with the discrete maximum principle K Lipnikov, D Svyatskiy, Y Vassilevski
Russian Journal of Numerical Analysis and Mathematical Modelling 27 (4), 369-386, 2012
93 2012 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
88 2011 A multilevel multiscale mimetic (M3) method for two-phase flows in porous media K Lipnikov, JD Moulton, D Svyatskiy
Journal of Computational Physics 227 (14), 6727-6753, 2008
82 2008 Anderson acceleration for nonlinear finite volume scheme for advection-diffusion problems K Lipnikov, D Svyatskiy, Y Vassilevski
SIAM Journal on Scientific Computing 35 (2), A1120-A1136, 2013
51 2013 Specifcation of the near-earth space environment with shields V Jordanova, GL Delzanno, MG Henderson, H Godinez, CA Jeffery, ...
Journal of Atmospheric and Solar-Terrestrial Physics, 2017
40 2017 Self-similar structure and experimental signatures of suprathermal ion distribution in inertial confinement fusion implosions G Kagan, D Svyatskiy, HG Rinderknecht, MJ Rosenberg, AB Zylstra, ...
Physical review letters 115 (10), 105002, 2015
36 2015 Advanced terrestrial simulator E Coon, D Svyatsky, A Jan, E Kikinzon, M Berndt, A Atchley, D Harp, ...
Computer Software, USDOE Office of Science (SC), Biological and …, 2019
35 2019 M-adaptation in the mimetic finite difference method V Gyrya, K Lipnikov, G Manzini, D Svyatskiy
Mathematical Models and Methods in Applied Sciences 24 (08), 1621-1663, 2014
22 2014 Second-order accurate finite volume schemes with the discrete maximum principle for solving Richards’ equation on unstructured meshes D Svyatskiy, K Lipnikov
Advances in water resources 104, 114-126, 2017
20 2017 New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation K Lipnikov, D Moulton, D Svyatskiy
Advances in water resources 94, 11-22, 2016
20 2016 Flow and transport in three-dimensional discrete fracture matrix models using mimetic finite difference on a conforming multi-dimensional mesh JD Hyman, MR Sweeney, CW Gable, D Svyatsky, K Lipnikov, JD Moulton
Journal of Computational Physics 466, 111396, 2022
19 2022 Ion kinetic dynamics in strongly-shocked plasmas relevant to ICF HG Rinderknecht, PA Amendt, MJ Rosenberg, CK Li, JA Frenje, ...
Nuclear Fusion 57 (6), 066014, 2017
18 2017 Adaptive Strategies in the Multilevel Multiscale Mimetic ( ) Method for Two-Phase Flows in Porous Media K Lipnikov, JD Moulton, D Svyatskiy
Multiscale Modeling & Simulation 9 (3), 991-1016, 2011
18 2011