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- Ilya D Mishev
- 2004

Two cell centered nite di erence schemes on Voronoi meshes are de rived and investigated Stability and error estimates in a discrete H norm for both symmetric and nonsymmetric problems including convec tion dominated are proven The theoretical results are illustrated with several numerical experiments

- O. V. DIYANKOV, S. V. KOSHELEV, +5 authors A. K. USADI
- 2007

SparSol is a software package intended for the preconditioned iterative solution of large sparse linear systems. It includes sets of iterative methods, preconditioners, scaling and reordering algorithms that allows to choose the optimal combination of algorithms for a particular problem. The paper briefly describes the algorithms implemented and numerically… (More)

- R D LAZAROV, ILYA D MISHEV
- 2004

Introduction In this paper we consider cell centered nite di erence approximations for second order convection di usion equations of divergence type Our goal is to construct nite di erence methods of second order of approximation that satisfy the discrete maximum principle The error estimates are in the discrete Sobolev spaces associated with the considered… (More)

We derive a novel finite volume method for the elliptic equation, using the framework of mixed finite element methods to discretize the pressure and velocities on two different grids (covolumes), triangular (tetrahedral) mesh and control volume mesh. The new discretization is defined for tensor diffusion coefficient and well suited for heterogeneous media.… (More)

- R. D. Lararov, I. D. Mishev, Panayot S. Vassilevski
- Computing
- 1994

Based on approximation of the balance relation for convection-diffusion problems, finite difference schemes on rectangular locally refined grids are derived and studied. A priori estimates and error bounds in discreteH 1-norm are provided. Numerical examples demonstrating the accuracy of the schemes for a variety of model convection-diffusion problems are… (More)

We derive and study cell centered nite volume approximations of reaction di usion equations For Voronoi and circumscribed volumes we obtain monotone schemes If the volumes satisfy regularity condition then the schemes are H positive de nite and rst order accurate For nite volumes satisfying an additional symmetry condition the schemes are second order… (More)

- I. D. Mishev
- 2008

SUMMARY Run-time performance of a reservoir simulator is significantly impacted by the selection of the linear solver preconditioner, iterative method and their adjustable parameters. The choice of the best solver algorithm and its optimal parameters is a difficult problem that even the experienced simulator users cannot adequately solve by themselves. The… (More)

- Ilya D. Mishev
- 2007

The error estimates for nite volume element method applied to 2 and 3-D non-deenite problems are derived. A simple upwind scheme is proven to be unconditionally stable and rst order accurate.

- ILYA D MISHEV
- 2004

We consider cell centered nite di erence discretizations with lo cal re nement for nonsymmetric boundary value problems Preconditioners with mesh independent convergence properties for corresponding matrices are constructed The method is illustrated with numerical experiments

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