o PUBLICATIONS (1995 - 2013)

2014
1. M-Adaptation in the mimetic finite difference method.
Math. Models Methods Appl. Sci. V.24, pp.1621-1663 (with V.Gyrya, G.Manzini, D.Svyatskiy).

2. Discontinuous Galerkin and Mimetic Finite Difference Methods for Coupled Stokes-Darcy Flows on Polygonal and Polyhedral Grids
Numerische Mathematik, V.126, Issue 2, pp.321-360 in press, (with I.Yotov, D.Vassilev)



2013
1. Second-order accurate monotone finite volume scheme for Richards' equation.
J. Comp. Phys., V.239, pp.123-137 (with O.Misitas).

2. On the reconstruction of Darcy velocity in finite volume methods.
Transport in Porous Media V.96, pp.337-351. (with G.Srinivasan).

3. Mimetic discretization of two-dimensional magnetic diffusion equations.
J. Comp. Phys., V.247, pp.1--16 (with J.Reynolds, E.Nelson).

4. High-order mimetic methods for unstructured polyhedral meshes.
Los Alamos Report LAUR-13-21171 (2013) (with G.Manzini).

5. Anderson acceleration for nonlinear finite volume scheme for advection-diffusion problems.
SIAM J Sci. Comp., in press (with D.Svyatskiy, Yu.Vassilevski).



2012
1. M-adaptation method for acoustic wave equation on square meshes.
J. Comp. Acoustics, V.20, No.4, pp.1250022-1:23 (with V.Gyrya).

2. Minimal stencil finite volume schme with the discrete maximum principle.
Russian J. Numer. Analysis Math. Modelling V.27, No.4, pp.369-385 (with D.Svyatskiy and Yu.Vassilevski).

3. Mimetic finite difference method.
Review paper. Los Alamos Report LAUR-12-24245, submitted to JCP (with G.Manzini and M.Shashkov).

4. ASCEM Pumping Test Capabilities: Benchmarking and Demonstration for UGTA at U--20 WW.
Los Alamos Report LAUR-12-26614 (with D.Harp, E.Kwicklis, A. Wolfsberg, J.Moulton, C.Gable, C.Walter, N.Becker, M. Berndt and V.Vesselinov).



2011
1. Adaptive strategies in the multilevel multiscale mimetic M3 method for two-phase flows in porous media.
Multiscale Modeling and Simulation, V.9, No.3, pp.991-1016 (with D.Moulton and D.Svyatskiy).

2. The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes.
J. Comp. Phys., V.230, No.2, pp.305-328 (with M.Manzini, F.Brezzi and A.Buffa).

3. Effective shear viscosity and dynamics of suspensions of micro-swimmers at moderate concentrations.
Journal of Mathematical Biology, (with V. Gyrya, I. Aronson, and L. Berlyand).

4. Families of meshes minimizing $P_1$ interpolation for functions with indefinite Hessian.
Russian J. Numer. Analysis Math. Modelling V.26, No.4, pp.337-352 (with A.Agouzal and Yu.Vassilevski).

5. Arbitrary order nodal mimetic discretizations of elliptic problems on polygonal meshes.
SIAM J. Numer. Anal. V.49, No.5, pp.1737-1760 (with L. Beirao da Veiga and G.Manzini).

6. On optimal convergence rate of finite element solutions of boundary value problems on adaptive anisotropic meshes.
Math. Comput. Simul. V.81, pp.1949-1961 (with A.Agouzal and Yu.Vassielvski).

7. Adaptation of mimetic finite difference discretization to reducing numerical dispersion in wave equation.
Proceedings of 10th Int. Conference on the Mathematical and Numerical Aspects of Waves, July 25-29, 2011, Vancouver, Canada, pp.343-346 (with V.Gyrya).

8. Benchmark 3D: Mimetic Finite difference Method for Generalized Polyhedral Meshes.
Springer Proceedings in Mathematics "Finite Volumes for Complex Applications VI Problems & Perspectives", Volume 2, J.Fort, J.Furst, J.Halama, R.Herbin, F.Hubert (Editors), Springer, pp.235-242 (with G.Manzini).

9. Monotonicity Conditions in the Mimetic Finite Difference Method.
Springer Proceedings in Mathematics "Finite Volumes for Complex Applications VI Problems & Perspectives", Volume 1, J.Fort, J.Furst, J.Halama, R.Herbin, F.Hubert (Editors), Springer, pp.653--662 (with G.Manzini and D.Svyatskiy).





2010
1. Error analysis for a mimetic discretization of the steady Stokes problem on polyhedral meshes.
SIAM J. Numer. Anal. V.48, No.4, pp.1419-1443 (with L.Beirao da Veiga and G.Manzini).

2. A framework for developing a mimetic tensor artificial viscosity for Lagrangian hydrocodes on arbitrary polygonal meshes.
J. Comp. Phys., V.229, pp.7911-7941 (with M.Shashkov).

3. A Mimetic Discretization of the Stokes Problem with Selected Edge Bubbles
SIAM J Sci. Comp., V.32, No.2, pp.875-893 (with L.Beirao da Veiga).

4. Hessian-free metric-based mesh adaptation via geometry of interpolation error
Computational Mathematics and Mathematical Physics, V.50, no.1, pp.131--145 (with A.Agouzal and Yu.Vassilevski).

5. A monotone finite volume scheme for advection-diffusion equations on unstructured polygonal meshes.
J. Comp. Phys., V.229, pp, 4017-4032 (with D.Svyatskiy and Yu.Vassielvski).

6. Solution of the diffusion equation in multi-material domains by subdivision of elements along reconstructed interfaces
International Journal for Numerical Methods in Fluids, published online (with R.Garimella).

7. On discrete boundaries and solution accuracy in anisotropic adaptive meshing.
Engrg. Computers, V.26, pp, 281-288 (with Yu.Vassilevski).

8. A multiscale multilevel mimetic (M3) method for well-driven flows in porous media.
Procedia Computer Science, V.1, Issue 1, pp.771-779 (with J.D. Moulton and D. Svyatskiy).

9. Edge-based a posteriori error estimators for generating quasi-optimal simplicial meshes.
Math. Mod. Nat. Phenom. V.5, No.7, pp. 91-96 (with A.Agouzal and Yu.Vassielvski).

10. A mimetic tensor artificial viscosity method for arbitrary polyhedral meshes.
Procedia Computer Science, V.1, Issue 1, pp.1915-1923 (with M.Shashkov).



2009
1. Convergence analysis of the high-order mimetic finite difference method.
Numerische Mathematik, V.113, No.3, pp.325--356. (with L.Beirao da Veiga and G.Manzini).

2. A multilevel multiscale mimetic (M$^3$) method for an anisotropic infiltration problem.
Lecture Notes in Computer Science, V.5544, Springer-Verlag, pp.685--694. (with J.Moulton and D.Svyatskiy).

3. Error estimates for a finite element solution of the diffusion equation based on composite norms.
J. Numer. Math., V.17, No.2, pp.77-95. (with A.Agouzal and Yu.Vassilevski).

4. Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes.
J. Comp. Phys., V.228, No.3, pp.703-716. (with D.Svyatskiy, and Yu.Vassilevski).

5. Local flux mimetic finite difference methods.
Numerische Mathematik V.112, No.1, pp.115-152. (with M.Shashkov and I.Yotov) (abstract) (request a copy).

6. Mimetic finite differences for elliptic problems.
M2AN: Math. Model. Numer. Anal. V.43, pp.277-295. (with F.Brezzi and A.Buffa).

7. Mimetic finite difference method for the Stokes problem on polygonal meshes.
J. Comp. Phys., V.228, No.19, pp.7215-7232. (with L.Beirao da Veiga, V.Gyrya and G.Manzini).

8. Anisotropic mesh adaptation for solution of finite element probems using hierarchical edge-based error estimates.
Proceedings of 18th International Meshing Roundtable, Salt Lake City, UT. B.Clark (Editor), Springer, pp.595--610. (with A.Agouzal and Yu.Vassilevski).



2008
1. High-order mimetic finite difference method for diffusion problem on polygonal meshes.
J. Comp. Phys., V.227, pp.8841-8854. (with V.Gyrya).

2. A Multilevel Multiscale Mimetic M3 Method for two-Phase Flows in Porous Media.
J. Comp. Phys., V.227, pp.6727-6753. (with D.Moulton and D.Svyatskiy).

3. Mimetic finite difference method.
Proceedings of 5th International Symposium on Finite Volumes for Complex Applications, June 8-13, 2008, Aussois, France; R.Eymard, J.-M.Herard (Editors), Wiley, pp.843--850.

4. Metric tensors for generation of optimal meshes.
Proceedings of Int. Conf. NUMGRID-2008, Computing center RAS, Moscow, pp.264--271. (with A.Agouzal and Yu.Vassilevski).



2007
1. Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes.
J. Comp. Phys., V.227, pp.492--512. (with M.Shashkov, D.Svyatskiy, and Yu.Vassilevski).

2. A new discretization methodology for diffusion problems on generalized polyhedral meshes.
Comput. Methods Appl. Mech. Engrg., V.196, pp.3682-3692. (with F.Brezzi, M.Shashkov, and V.Simoncini) (PDF).

3. Generation of quasi-optimal meshes based on a posteriori error estimates.
Proceedings of 16th International Meshing Roundtable, WA. M.Brewer, D.Marcum (Editors), Springer, 2007, pp.139--148. (with A.Agouzal and Yu.Vassilevski).



2006
1. The Error-Minimization-based strategy for moving mesh methods.
Communications in Computational Physics V.1, No.1, pp.53--81 (with M.Shashkov) (abstract) (request a copy).

2. The error-minimization-based rezone strategy for arbitrary Lagrangian-Eulerian methods.
Numerical Methods for Partial Differential Equations V.22, No.3, pp.617-637 (with M.Shashkov) (abstract) (PDF)

3. Convergence of mimetic finite difference method for diffusion problems on polyhedral meshes with curved faces.
M3AS: Mathematical Models and Methods in Applied Sciences V.16, No.2, pp.275--297 (with F.Brezzi and M.Shashkov) (abstract) (request a copy).

4. The mimetic finite difference discretization of diffusion problem on unstructured polyhedral meshes.
J. Comp. Phys., V.211, pp.473--491 (with M.Shashkov and D.Svyatskiy) (abstract) (request a copy)

5. Analysis of Hessian recovery methods for generating adaptive meshes.
Proceedings of 15th International Meshing Roundtable, P.Pebay (Editor), Springer, Berlin, Heidelberg, New York, 2006, pp.163--171. (with Yu.Vassivelski).

6. Hessian recovery method for adaptive mesh generation.
Voprosy Atomnoj Nauki i Tehniki. Ser. "Mathematical modeling of physical processes". V.3, pp.37--53. (with Yu.Vassilevski).



2005
1. Convergence of mimetic finite difference method for diffusion problems on polyhedral meshes.
SIAM J. Numer. Anal. V.43, No.5, pp.1872--1896. (with F.Brezzi and M.Shashkov) (abstract) (request a copy).

2. A mortar mimetic finite difference method on non-matching grids.
Numerische Mathematik V.102, No.2, pp.203--230. (with M.Berndt, M.Shashkov, M.Wheeler, and I.Yotov) (PDF)

3. A node reconnection algorithm for mimetic finite difference discretizations of elliptic equations on triangular meshes.
Communications in Mathematical Sciences. V.3, No.4. pp.665--680. (with M.Berndt, M.Shashkov, and P.Vachal) (abstract) (request a copy)

4. Superconvergence of the velocity in mimetic finite difference methods on quadrilaterals.
SIAM J. Numer. Anal. V.43, No.4, pp.1728--1749 (with M.Berndt, M.Shashkov, M.Wheeler, and I.Yotov) (PDF)

5. A family of mimetic finite difference methods on polygonal and polyhedral meshes.
M3AS: Mathematical Models and Methods in Applied Sciences V.15, No.10, pp. 1533--1552 (with F.Brezzi and V.Simoncini) (abstract) (Los Alamos Report 05-1061)

6. Hessian based anisotropic mesh adaptation in domains with discrete boundaries.
Russian J. Numer. Analysis Math. Modelling V.20, No.4, pp. 391--402 (with V. Dyadechko and Yu. Vassilevski) (request a copy).

7. Error bounds for controllable adaptive algorithms based on a Hessian recovery.
Computational Mathematics and Mathematical Physics, V.45, No.8, pp. 1374--1384 (with Yu.Vassilevski) (request a copy)



2004
1. Mimetic finite difference method on polygonal meshes for diffusion-type problems.
Comp. Geosciences V.8, No.4, pp. 301--324 (with Yu.Kuznetsov and M.Shashkov) (abstract) (request a copy)

2. Error Estimates for Hessian-based mesh adaptation algorithms with control of adaptivity.
Proceedings of 13th International Meshing Roundtable, September 19-22, Williamsburg, Virginia, pp.345-351 (with Yu.Vassilevski) (paper)

3. On a parallel algorithm for controlled Hessian-based mesh adaptation.
Proceedings of 3rd Conf. Appl. Geometry, Mesh Generation and High Performance Computing, Moscow, June 28 - July 1, Comp. Center RAS, V.1, pp.154-166 (with Yu.Vassilevski)

4. Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes.
J. Comp. Phys., (with J.Morel and M.Shashkov) (abstract)

5. On control of adaptation in parallel mesh generation.
Engrg. Computers, V.20, pp.193-201, (with Yu.Vassilevski) (abstract)



2003
1. Mathematics modeling and numerical algorithms for poroelastic problems.
Contemporary Mathematics, V.329, pp.191-202, (with Yu.Kuznetsov, S.Lyons and S. Maliassov) (abstract)

2. Optimal triangulations: existence, approximation and double differentiation of $P_1$ finite element functions.
Computational Mathematics and Mathematical Physics, V.43, No.6, pp.827-835, (with Yu.Vassilevski) (abstract)

3. Nested grid iteration for incompressible viscous flow and transport.
Inter. J. Comp. Fluid Dynamics, V.17, No.4, pp.253-262, (with B.Kirk and G.Carey) (abstract)

4. Parallel adaptive solution of 3D boundary value problems by Hessian recovery.
Comput. Methods Appl. Mech. Engrg., V.192, pp. 1495-1513, (with Y.Vassilevski) (abstract)

5. Moving grids for hyperbolic problems.
Proceedings of the Workshop on Mesh Quality and Dynamic Meshing, January 16-17, Sandia National Laboratory, CA, USA, (with M.Shashkov) (abstract)



2002
1. A subspace cascadic multigrid method for mortar elements.
Computing, V.69, No.3, pp.205-225, (with D.Braess and P.Deuflhard) (abstract)

2. Fast separable solver for mixed finite element methods and applications.
J. Numer. Math., V.10, No.2, pp. 137-155, (with Yu.Kuznetsov) (abstract)

3. Fictitious domain based solvers for particulate flows.
Proceedings of the 13th International Conference on DD Methods, October 2000, Lyon, France, pp.351--357, (with D.Dashevski, R.Glowinski and Yu.Kuznetsov) (abstract)



2001
1. Convergence of mimetic finite difference discretizations of the diffusion equation.
J. Numer. Math., V.9, No.4, pp.265-284. (with M.Berndt, D.Moulton and M.Shashkov ) (PDF)



2000
1. An efficient iterative solver for a simplified poroelasticity problem.
East-West Journal, V.8, No.3, pp. 207-222. (with Yu.Kuznetsov ) (abstract)



1999
1. Adaptive generation of quasi-optimal tetrahedral meshes.
East-West Journal, V.7,No.4, pp. 223-244. (with A.Agouzal and Y.Vassilevski) (abstract)

2. An adaptive algorithm for quasioptimal mesh generation.
Computational Mathematics and Mathematical Physics, V.39, No.9, pp.1468-1486. (with Yu.Vasilevskii) (abstract)



1998
1. Fictitious domain methods for the numerical solution of 3D acoustic scattering problems.
J. Comp. Acoustics, V.7, No.3, pp.161-183. (with Yu.Kuznetsov and E.Heikkola ) (abstract)

2. 3D Helmholtz wave equation by fictitious domain method.
Russian J. Numer. Analysis Math. Modelling, V.13, No.5, 371-389. (with Yu.Kuznetsov ) (abstract)



1997
1. Domain decomposition with subdomain CCG for material jump elliptic problems.
East-West Journal, V.6, No.2, 81-100. (with P.Deuflhard ) (abstract)

2. Finite element methods with nonmatching grids and applications.
Proceedings of the Conference on Applied Mathematics and Computer Science, 28-29 October 1996, Moscow, Russia, French-Russian A.M.Liapunov Institute, Moscow State University, pp.65-81. (with G.S. Abdoulaev, Y. Achdou, Yu.A.Kuznetsov , J. Periaux and O.Pironneau ) (abstract)



1996
1. On using parallel MIMD computer systems in the inverse problem of acoustic scattering.
RIM-GARC Preprint, Series 96-27, pp.1-20. (abstract)



1995
1. On the application of fictitious domain and domain decomposition methods for scattering problems on Cray Y-MP C98.
Report No.9557, University of Nijmegen, The Netherlands. (with Yu.Kuznetsov ) (abstract)