On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes
نویسنده
چکیده
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes Pascal Omnes
منابع مشابه
On the Second-order Convergence of Finite Volume Methods for the Laplace Equation on Delaunay-voronoi Meshes
Abstract. Cell-centered and vertex-centered finite volume schemes for the Laplace equation with homogeneous Dirichlet boundary conditions are considered on triangular meshes and their Voronoi duals. On a two-dimensional convex polygonal domain, it is shown that a suitable combination of the solutions of these two schemes converges with second-order accuracy towards the exact solution in the L n...
متن کاملVoronoi - based finite volume methods , optimal Voronoi meshes , and PDEs on the sphere q
We first develop and analyze a finite volume scheme for the discretization of partial differential equations (PDEs) on the sphere; the scheme uses Voronoi tessellations of the sphere. For a model convection–diffusion problem, the finite volume scheme is shown to produce first-order accurate approximations with respect to a mesh-dependent discrete firstderivative norm. Then, we introduce the not...
متن کاملSeepage with Nonlinear Permeability by Least Square FEM
In seepage problems, the coefficients of permeability in Laplace equation are usually assumed to be constant vs. both space and time; but in reality these coefficients are variable. In this study, the effect of material deformation due to external loads (consolidation) and variation of head in the consolidation process are considered. For the first case, formulation of kx and ky can be defined ...
متن کاملPressure-Velocity Coupled Finite Volume Solution of Steady Incompressible Invscid Flow Using Artificial Compressibility Technique
Application of the computer simulation for solving the incompressible flow problems motivates developing efficient and accurate numerical models. The set of Inviscid Incompressible Euler equations can be applied for wide range of engineering applications. For the steady state problems, the equation of continuity can be simultaneously solved with the equations of motion in a coupled manner using...
متن کاملA Finite Volume Method for the Laplace Equation on Almost Arbitrary Two-dimensional Grids
We present a finite volume method based on the integration of the Laplace equation on both the cells of a primal almost arbitrary two-dimensional mesh and those of a dual mesh obtained by joining the centers of the cells of the primal mesh. The key ingredient is the definition of discrete gradient and divergence operators verifying a discrete Green formula. This method generalizes an existing f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011