Publisher Summary This chapter focuses on finite volume methods. The finite volume
method is a discretization method that is well suited for the numerical simulation of various …

We present Finite Volume methods for diffusion equations on generic meshes, that received
important coverage in the last decade or so. After introducing the main ideas and …

This text presents a comprehensive mathematical theory for elliptic, parabolic, and
hyperbolic differential equations. It compares finite element and finite difference methods …

The finite volume element method (FVE) is a discretization technique for partial differential
equations. It uses a volume integral formulation of the problem with a finite partitioning set of …

Finite volume methods are a class of discretization schemes resulting from the
decomposition of a problem domain into nonoverlapping control volumes. Degrees of …

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 …

In this paper we consider covolume or finite volume element methods for variable coefficient
elliptic and parabolic problems on convex smooth domains in the plane. We introduce a …

A key ingredient in simulation of flow in porous media is accurate determination of the
velocities that drive the flow. Large‐scale irregularities of the geology (faults, fractures, and …

An error analysis of a family of cell-center finite volume schemes for Poisson's equation on
Cartesian product nonuniform meshes in two dimensions is presented. Optimal-order error …

We propose and analyze a numerical scheme for nonlinear degenerate parabolic
convection–diffusion–reaction equations in two or three space dimensions. We discretize …