Derivation, stability and error analysis in both discrete H 1 and L 2 norms for cell-centered nite volume approximations of convection-diiusion problems are presented. Various up-wind strategies are investigated. The theoretical results are illustrated by numerical examples.
Two cell-centered nite diierence schemes on Voronoi meshes are derived and investigated. Stability and error estimates in a discrete H 1-norm for both symmetric and nonsymmetric problems, including convec-tion dominated, are proven. The theoretical results are illustrated with several numerical experiments.
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)
— 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… (More)
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)
We consider cell-centered nite diierence discretizations with local reenement for nonsymmetric boundary value problems. Preconditioners with mesh independent convergence properties for corresponding matrices are constructed. The method is illustrated with numerical experiments. 1. Introduction This paper is devoted to construction of preconditioners of… (More)