An implicit approximate inverse preconditioner for saddle point problems.
An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
In this article, we consider the initial value problem which is obtained after a space discretization (with space step ) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between and the time step size...
An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
In this article, we consider the initial value problem which is obtained after a space discretization (with space step h) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size h chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between h and the time...
An incomplete-factorization preconditioning using repeated red-black ordering.
An introduction to hierarchical matrices
An introduction to hierarchical matrices
We give a short introduction to a method for the data-sparse approximation of matrices resulting from the discretisation of non-local operators occurring in boundary integral methods or as the inverses of partial differential operators. The result of the approximation will be the so-called hierarchical matrices (or short -matrices). These matrices form a subset of the set of all matrices and have a data-sparse representation. The essential operations for these matrices (matrix-vector and matrix-matrix...
An Iteration Method for Studying the Bifurcation of Solutions of the Nonlinear Equations, L(...) u + ..R (..., u) = 0 .
An Iteration Scheme for Boundary Value-Alternative Problems.
An iterative method of alternating type for systems with special block matrices
An iterative procedure for systems with matrices originalting from the domain decomposition technique is proposed. The procedure introduces one iteration parameter. The convergence and optimization of the method with respect to the parameter is investigated. The method is intended not as a preconditioner for the CG method but for the independent use.
An Iterative Substructuring Algorithm for Equilibrium Equations.
An estimate and a superconvergence result for a Galerkin method for elliptic equations based on tensor products of piecewise polynomials
An L2-Error Estimate for an Approximation of the Solution of a Parabolic Variational Inequality.
An operator method for a numerical quadrature finite element approximation for a class of second-order elliptic eigenvalue problems in composite structures
An optimal method of Galerkin type for diffusion-dispersion problems.
An Optimal Order Multigrid Method for Biharmonic, C1 Finite Element Equations.
An unconditionally stable finite element-finite volume pressure correction scheme for the drift-flux model
We present in this paper a pressure correction scheme for the drift-flux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is conservative, the unknowns are kept within their physical bounds and, in the homogeneous case (i.e. when the drift velocity vanishes), the discrete entropy of the system decreases; in addition, when using for the drift velocity a closure law which takes the form of...
An unconditionally stable pressure correction scheme for the compressible barotropic Navier-Stokes equations
We present in this paper a pressure correction scheme for the barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the continuous problem also hold for the discrete solution. The stability proof is based on two independent results for general finite volume discretizations, both interesting for their own sake: the L2-stability of the discrete advection operator provided it...
An up-wind finite element method for a filtration problem
An upwind finite element method for singularly perturbed elliptic problems and local estimates in the -norm
An upwinding mixed finite element method for a mean field model of superconducting vortices