The stability and convergence properties of the mimetic finite difference method for diffusion-type problems on polyhedral meshes are analyzed. The optimal convergence rates for the scalar and vectorâ€¦ (More)

The principal goal of all numerical algorithms is to represent as faithfully and accurately as possible the underlying continuum equations to which a numerical solution is sought. However, in theâ€¦ (More)

In this paper we present a new formulation of the artificial viscosity concept. Physical arguments for the origins of this term are given and a set of criteria that any proper functional form of theâ€¦ (More)

operators, in this case, the divergence =? and the gradient =: A finite-difference algorithm for the numerical solution of diffusion problems in strongly heterogeneous and nonisotropic media isâ€¦ (More)

We developed multi-material (more than two materials) interface reconstruction methods for 3D meshes of generalized polyhedrons, [ 1]. The basic information used in interface reconstruction is theâ€¦ (More)

The maximum principle is a basic qualitative property of the solution of second-order elliptic boundary value problems. The preservation of the qualitative characteristics, such as the maximumâ€¦ (More)

We derive a cell-centered 2-D diffusion differencing scheme for arbitrary quadrilateral meshes in r-z geometry using a local support-operator method. Our method is said to be local because it yieldsâ€¦ (More)

We designed a new volume-conservative interface reconstruction method. An input data set for the interface reconstruction algorithm consists of volumes and centroids of the cell fractions occupied byâ€¦ (More)

The bane of Lagrangian hydrodynamics calculations is the premature breakdown of grid topology that results in severe degradation of accuracy and run termination often long before the assumption of aâ€¦ (More)

A new second-order finite-difference algorithm for the numerical where nW is the vector of unit outward normal to the boundsolution of diffusion problems in strongly heterogeneous and nonary ÂV, andâ€¦ (More)