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 | 249 | 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 | 162 | 2009 |

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 | 114 | 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 | 92 | 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 | 82 | 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 | 79 | 2016 |

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 | 78 | 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 | 75 | 2008 |

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 | 75 | 2008 |

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 | 73 | 2012 |

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 | 35 | 2013 |

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 | 27 | 2015 |

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 | 25 | 2021 |

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 |

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 | 21 | 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 | 17 | 2011 |

Monotonicity conditions in the mimetic finite difference method K Lipnikov, G Manzini, D Svyatskiy Finite Volumes for Complex Applications VI Problems & Perspectives, 653-661, 2011 | 12 | 2011 |

Mesh adaptation and discrete maximum principle for 2D anisotropic diffusion problems XP Li, D Svyatskiy, M Shashkov Technical Report LA-UR 10-01227, Los Alamos National Laboratory, Los Alamos, NM, 2007 | 12 | 2007 |

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 | 11 | 2017 |

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 | 11 | 2017 |