Derivation, stability, and error analysis in both discrete H^1-and L^2-norms for cell-centered
finite volume approximations of convection-diffusion problems are presented. Various …

A cell-centered finite volume method is proposed to approximate numerically the solution to
the steady convection-diffusion equation on unstructured meshes of d-simplexes, where …

This book develops a systematic and rigorous mathematical theory of finite difference
methods for linear elliptic, parabolic and hyperbolic partial differential equations with …

A MUSCL-like cell-centered finite volume method is proposed to approximate the solution of
multi-dimensional steady advection–diffusion equations. The second-order accuracy is …

In this paper we study the convergence of a centred finite difference scheme on a non-
uniform mesh for a 1D elliptic problem subject to general boundary conditions. On a non …

Locally conservative, finite volume-type methods based on continuous piecewise
polynomial functions of degree r ≥ 2 are introduced and analyzed in the context of indefinite …

We consider a Dirichlet boundary-value problem for the three-dimensional convection-
diffusion equations with constant coefficients in the unit cube. A high order compact finite …

We construct an usual linearized difference scheme for initial boundary value problems
(IBVP) for one-dimensional quasilinear parabolic equations with generalized solutions. The …

In this paper, we study the convergence of a finite difference scheme on nonuniform grids for
the solution of second-order elliptic equations with mixed derivatives and variable …

In this paper we study the convergence properties of a cell-centered finite difference scheme
for second order elliptic equations with variable coefficients subject to Dirichlet boundary …