Convergence of mimetic finite difference discretizations of the diffusion equation. - Markus Berndt; Konstantin Lipnikov; J. David Moulton; Mikhail J. Shashkov (J. Num. Math., 2001)

A Subspace Cascadic Multigrid Method for Mortar Elements. - Dietrich Braess; Peter Deuflhard; Konstantin Lipnikov (Computing, 2002)

Fast separable solver for mixed finite element methods and applications. - Yuri A. Kuznetsov; Konstantin Lipnikov (J. Num. Math., 2002)

Error Estimates for Hessian-Based Mesh Adaptation Algorithms with Control of Adaptivity. - Konstantin Lipnikov; Yuri V. Vassilevski (IMR, 2004)

On control of adaptation in parallel mesh generation. - Konstantin Lipnikov; Yuri V. Vassilevski (Eng. Comput., 2004)

A mortar mimetic finite difference method on non-matching grids. - Markus Berndt; Konstantin Lipnikov; Mikhail J. Shashkov; Mary F. Wheeler; Ivan Yotov (Numerische Mathematik, 2005)

Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals. - Markus Berndt; Konstantin Lipnikov; Mikhail J. Shashkov; Mary F. Wheeler; Ivan Yotov (SIAM J. Numer. Anal., 2005)

Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes. - Franco Brezzi; Konstantin Lipnikov; Mikhail J. Shashkov (SIAM J. Numer. Anal., 2005)

Analysis of Hessian Recovery Methods for Generating Adaptive Meshes. - Konstantin Lipnikov; Yuri V. Vassilevski (IMR, 2006)

Generation of Quasi-Optimal Meshes Based on a Posteriori Error Estimates. - Abdellatif Agouzal; Konstantin Lipnikov; Yuri V. Vassilevski (IMR, 2007)

Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes. - Konstantin Lipnikov; Mikhail J. Shashkov; Daniil Svyatskiy; Yuri V. Vassilevski (J. Comput. Phys., 2007)

High-order mimetic finite difference method for diffusion problems on polygonal meshes. - Vitaliy Gyrya; Konstantin Lipnikov (J. Comput. Phys., 2008)

A multilevel multiscale mimetic (M3) method for two-phase flows in porous media. - Konstantin Lipnikov; J. David Moulton; Daniil Svyatskiy (J. Comput. Phys., 2008)

A Multilevel Multiscale Mimetic (M3) Method for an Anisotropic Infiltration Problem. - Konstantin Lipnikov; J. David Moulton; Daniil Svyatskiy (ICCS (1), 2009)

Anisotropic Mesh Adaptation for Solution of Finite Element Problems Using Hierarchical Edge-Based Error Estimates. - Abdellatif Agouzal; Konstantin Lipnikov; Yuri V. Vassilevski (IMR, 2009)

Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes. - Konstantin Lipnikov; Daniil Svyatskiy; Yuri V. Vassilevski (J. Comput. Phys., 2009)

Mimetic finite difference method for the Stokes problem on polygonal meshes. - L. Beirão da Veiga; Vitaliy Gyrya; Konstantin Lipnikov; Gianmarco Manzini (J. Comput. Phys., 2009)

Error estimates for a finite element solution of the diffusion equation based on composite norms. - Abdellatif Agouzal; Konstantin Lipnikov; Yuri V. Vassilevski (J. Num. Math., 2009)

Local flux mimetic finite difference methods. - Konstantin Lipnikov; Mikhail J. Shashkov; Ivan Yotov (Numerische Mathematik, 2009)

Convergence analysis of the high-order mimetic finite difference method. - Lourenço Beirão da Veiga; Konstantin Lipnikov; Gianmarco Manzini (Numerische Mathematik, 2009)

On discrete boundaries and solution accuracy in anisotropic adaptive meshing. - Konstantin Lipnikov; Yuri V. Vassilevski (Eng. Comput., 2010)

A framework for developing a mimetic tensor artificial viscosity for Lagrangian hydrocodes on arbitrary polygonal meshes. - Konstantin Lipnikov; Mikhail J. Shashkov (J. Comput. Phys., 2010)

A monotone finite volume method for advection-diffusion equations on unstructured polygonal meshes. - Konstantin Lipnikov; Daniil Svyatskiy; Yuri V. Vassilevski (J. Comput. Phys., 2010)

A multiscale multilevel mimetic (M3) method for well-driven flows in porous media. - Konstantin Lipnikov; J. David Moulton; Daniil Svyatskiy (ICCS, 2010)

A mimetic tensor artificial viscosity method for arbitrary polyhedral meshes. - Konstantin Lipnikov; Mikhail J. Shashkov (ICCS, 2010)

Error Analysis for a Mimetic Discretization of the Steady Stokes Problem on Polyhedral Meshes. - L. Beirão da Veiga; Konstantin Lipnikov; Gianmarco Manzini (SIAM J. Numer. Anal., 2010)

A Mimetic Discretization of the Stokes Problem with Selected Edge Bubbles. - L. Beirão da Veiga; Konstantin Lipnikov (SIAM J. Sci. Comput., 2010)

Families of Meshes Minimizing P 1 Interpolation Error. - Abdellatif Agouzal; Konstantin Lipnikov; Yuri V. Vassilevski (IMR, 2011)

The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes. - Konstantin Lipnikov; Gianmarco Manzini; Franco Brezzi; Annalisa Buffa (J. Comput. Phys., 2011)

Analysis of the monotonicity conditions in the mimetic finite difference method for elliptic problems. - Konstantin Lipnikov; Gianmarco Manzini; Daniil Svyatskiy (J. Comput. Phys., 2011)

On optimal convergence rate of finite element solutions of boundary value problems on adaptive anisotropic meshes. - Abdellatif Agouzal; Konstantin Lipnikov; Yuri V. Vassilevski (Math. Comput. Simul., 2011)

Adaptive Strategies in the Multilevel Multiscale Mimetic (M3) Method for Two-Phase Flows in Porous Media. - Konstantin Lipnikov; J. David Moulton; Daniil Svyatskiy (Multiscale Model. Simul., 2011)

Arbitrary-Order Nodal Mimetic Discretizations of Elliptic Problems on Polygonal Meshes. - L. Beirão da Veiga; Konstantin Lipnikov; Gianmarco Manzini (SIAM J. Numer. Anal., 2011)

Mimetic discretization of two-dimensional magnetic diffusion equations. - Konstantin Lipnikov; James Reynolds; Eric Nelson (J. Comput. Phys., 2013)

Second-order accurate monotone finite volume scheme for Richards' equation. - Oleksandr Misiats; Konstantin Lipnikov (J. Comput. Phys., 2013)

Anderson Acceleration for Nonlinear Finite Volume Scheme for Advection-Diffusion Problems. - Konstantin Lipnikov; Daniil Svyatskiy; Yuri V. Vassilevski (SIAM J. Sci. Comput., 2013)

A high-order mimetic method on unstructured polyhedral meshes for the diffusion equation. - Konstantin Lipnikov; Gianmarco Manzini (J. Comput. Phys., 2014)

Mimetic finite difference method. - Konstantin Lipnikov; Gianmarco Manzini; Mikhail J. Shashkov (J. Comput. Phys., 2014)

A Lagrangian staggered grid Godunov-like approach for hydrodynamics. - Nathaniel R. Morgan; Konstantin Lipnikov; Donald E. Burton; Mark A. Kenamond (J. Comput. Phys., 2014)

Discontinuous Galerkin and mimetic finite difference methods for coupled Stokes-Darcy flows on polygonal and polyhedral grids. - Konstantin Lipnikov; Danail Vassilev; Ivan Yotov (Numerische Mathematik, 2014)

The mimetic finite difference method for elliptic and parabolic problems with a staggered discretization of diffusion coefficient. - Konstantin Lipnikov; Gianmarco Manzini; J. David Moulton; Mikhail J. Shashkov (J. Comput. Phys., 2016)

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor. - Vitaliy Gyrya; Konstantin Lipnikov (J. Comput. Phys., 2017)

Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces. - Evgeny Kikinzon; Yuri A. Kuznetsov; Konstantin Lipnikov; Mikhail J. Shashkov (J. Comput. Phys., 2017)

The mimetic finite difference method for the Landau-Lifshitz equation. - Eugenia Kim; Konstantin Lipnikov (J. Comput. Phys., 2017)

Convergence Analysis of the mimetic Finite Difference Method for Elliptic Problems with Staggered Discretizations of Diffusion Coefficients. - Gianmarco Manzini; Konstantin Lipnikov; J. David Moulton; Mikhail J. Shashkov (SIAM J. Numer. Anal., 2017)

A high-order discontinuous Galerkin method for level set problems on polygonal meshes. - Konstantin Lipnikov; Nathaniel R. Morgan (J. Comput. Phys., 2019)

A high-order conservative remap for discontinuous Galerkin schemes on curvilinear polygonal meshes. - Konstantin Lipnikov; Nathaniel R. Morgan (J. Comput. Phys., 2019)

Verification benchmarks for single-phase flow in three-dimensional fractured porous media. - Inga Berre; Wietse M. Boon; Bernd Flemisch; Alessio Fumagalli; Dennis Gläser; Eirik Keilegavlen; Anna Scotti; Ivar Stefansson; Alexandru Tatomir; Konstantin Brenner; Samuel Burbulla; Philippe R. B. Devloo; et al. (CoRR, 2020)

Conservative high-order discontinuous Galerkin remap scheme on curvilinear polyhedral meshes. - Konstantin Lipnikov; Nathaniel R. Morgan (J. Comput. Phys., 2020)

Multidimensional Staggered Grid Residual Distribution Scheme for Lagrangian Hydrodynamics. - Rémi Abgrall; Konstantin Lipnikov; Nathaniel R. Morgan; Svetlana V. Tokareva (SIAM J. Sci. Comput., 2020)

Flow and Transport in Three-Dimensional Discrete Fracture Matrix Models using Mimetic Finite Difference on a Conforming Multi-Dimensional Mesh. - Jeffrey D. Hyman; Matthew R. Sweeney; Carl W. Gable; Daniil Svyatskiy; Konstantin Lipnikov; J. David Moulton (CoRR, 2021)

Flow and transport in three-dimensional discrete fracture matrix models using mimetic finite difference on a conforming multi-dimensional mesh. - Jeffrey D. Hyman; Matthew R. Sweeney; Carl W. Gable; Daniil Svyatsky; Konstantin Lipnikov; J. David Moulton (J. Comput. Phys., 2022)

Conservative remapping of material-dependent fields between possibly misaligned material regions. - Hoby Rakotoarivelo; Rao V. Garimella; Angela Herring; Mikhail J. Shashkov; Daniel W. Shevitz; Evgeny Kikinzon; Jan Velechovský; Konstantin Lipnikov; Navamita Ray (J. Comput. Phys., 2022)

Multi-material swept face remapping on polyhedral meshes. - Jan Velechovský; Evgeny Kikinzon; Navamita Ray; Hoby Rakotoarivelo; Angela Herring; Mack Kenamond; Konstantin Lipnikov; Mikhail Yu. Shashkov; Rao V. Garimella; Daniel W. Shevitz (J. Comput. Phys., 2022)

A mimetic finite difference based quasi-static magnetohydrodynamic solver for force-free plasmas in tokamak disruptions. - Zakariae Jorti; Qi Tang 001; Konstantin Lipnikov; Xian-Zhu Tang (CoRR, 2023)

Conservative high-order data transfer method on generalized polygonal meshes. - Konstantin Lipnikov; Mikhail J. Shashkov (J. Comput. Phys., 2023)

Applying an Oriented Divergence Theorem to Swept Face Remap. - Jennifer Vaccaro; Konstantin Lipnikov (SIAM J. Numer. Anal., 2023)

An adaptive Newton-based free-boundary Grad-Shafranov solver. - Daniel A. Serino; Qi Tang 001; Xian-Zhu Tang; Tzanio V. Kolev; Konstantin Lipnikov (CoRR, 2024)