Properties of solutions of some finite-difference systems with variable coefficients

2000 ◽  
Vol 36 (11) ◽  
pp. 1704-1710 ◽  
Author(s):  
V. B. Kolmanovskii ◽  
N. P. Kosareva
Keyword(s):  
Finite Difference ◽  
Variable Coefficients ◽  
Difference Systems

Method of corrections by higher order differences for elliptic equations with variable coefficients

2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Givi Berikelashvili ◽  
Bidzina Midodashvili
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Convergence Rate ◽  
Difference Scheme ◽  
Elliptic Equations ◽  
Variable Coefficients ◽  
Order Accuracy ◽  
Corrected Scheme

AbstractWe consider the Dirichlet problem for an elliptic equation with variable coefficients, the solution of which is obtained by means of a finite-difference scheme of second order accuracy. We establish a two-stage finite-difference method for the posed problem and obtain an estimate of the convergence rate consistent with the smoothness of the solution. It is proved that the solution of the corrected scheme converges at rate

scholarly journals Supraconvergence of a Finite Difference Scheme for Elliptic Boundary Value Problems of the Third Kind in Fractional Order Sobolev Spaces

2006 ◽  
Vol 6 (2) ◽  
pp. 154-177 ◽  
Author(s):  
E. Emmrich ◽  
R.D. Grigorieff
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Elliptic Boundary ◽  
Special Kind ◽  
Variable Coefficients ◽  
Second Order ◽  
Nonuniform Grids ◽  
Close Relationship

AbstractIn this paper, we study the convergence of the finite difference discretization of a second order elliptic equation with variable coefficients subject to general boundary conditions. We prove that the scheme exhibits the phenomenon of supraconvergence on nonuniform grids, i.e., although the truncation error is in general of the first order alone, one has second order convergence. All error estimates are strictly local. Another result of the paper is a close relationship between finite difference scheme and linear finite element methods combined with a special kind of quadrature. As a consequence, the results of the paper can be viewed as the introduction of a fully discrete finite element method for which the gradient is superclose. A numerical example is given.

scholarly journals FINITE DIFFERENCE SOLUTION OF TWO-DIMENSIONAL SOLUTE TRANSPORT WITH PERIODIC FLOW IN HOMOGENOUS POROUS MEDIA

2017 ◽  
Vol 8 (2) ◽  
Author(s):  
Alexandar Djordjevich ◽  
Svetislav Savović ◽  
Aco Janićijević
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Variable Coefficients ◽  
Two Dimensional ◽  
Seepage Velocity ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Explicit Finite Difference ◽  
Explicit Finite Difference Method

Two-dimensional advection-diffusion equation with variable coefficients is solved by the explicit finite-difference method for the transport of solutes through a homogeneous, finite, porous, two-dimensional, domain. Retardation by adsorption, periodic seepage velocity, and a dispersion coefficient proportional to this velocity are permitted. The transport is from a pulse-type point source (that ceases after a period of activity). Included are the first-order decay and zero-order production parameters proportional to the seepage velocity, periodic boundary conditions at the origin and the end of the domain. Results are compared to analytical solutions reported in the literature for special cases and a good agreement was found. The solute concentration profile is greatly influenced by the periodic velocity fluctuations. Solutions for a variety of combinations of unsteadiness of the coefficients in the advection-diffusion equation are obtainable as particular cases of the one demonstrated here. This further attests to the effectiveness of the explicit finite difference method for solving two-dimensional advection-diffusion equation with variable coefficients in a finite media, which is especially important when arbitrary initial and boundary conditions are required.

Sign in / Sign up

Export Citation Format

Share Document