o Selected publications (1995 - 2008)

2008
1. High-order mimetic finite difference method for diffusion problem on polygonal meshes.
to appear in 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. Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes. Los Alamos Report LAUR-08-3000. Submitted to J. Comp. Phys. (with D.Svyatskiy, and Yu.Vassilevski).

4. Local flux mimetic finite difference methods.
Los Alamos Report LAUR-08-0651. Submitted to Numer. Math. (with M.Shashkov and I.Yotov) (abstract) (request a copy).

5. Mimetic finite differences for elliptic problems.
M2AN: Math. Model. Numer. Anal.(accepted) (with F.Brezzi and A.Buffa).

6. Metric-based control of mesh adaptation in arbitrary Lagrangian Eulerian simulations.
Los Alamos Report LAUR-06-4765 (with Yu.Vassilevski)

7. A new discretization scheme on polyhedral grids for diffusion problems.
Los Alamos Report LAUR-06-3727 (with J.Morel and S.Runnels)

8. 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.

9. Error estimates for a finite element solution of the diffusion equation based on composite norms.
Los Alamos Report LAUR 08-1810. Submitted to J. Numer. Math. (with A.Agouzal and Yu.Vassilevski).

10. Convergence analysis of the high-order mimetic finite difference method.
Los Alamos Report LAUR 08-4601. Submitted to Numer. Math. (with B. deVeiga and M.Manzini).



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. On discrete boundaries and solution accuracy in anisotropic adaptive meshing.
Engrg. Computers, accepted (with Yu.Vassilevski).

4. 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., V.199, pp.589-597, (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.
East-West 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)