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 …

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

We present a general error estimation framework for a finite volume element (FVE) method
based on linear polynomials for solving second-order elliptic boundary value problems. This …

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 …

Node‐based uniform strain elements for three‐node triangular and four‐node tetrahedral
meshes are presented. The elements use the linear interpolation functions of the original …

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 …

This paper is devoted to analysis of some convergent properties of both linear and quadratic
simplicial finite volume methods (FVMs) for elliptic equations. For linear FVM on domains in …

Two cell‐centered finite difference schemes on Voronoi meshes are derived and
investigated. Stability and error estimates in a discrete H1‐norm for both symmetric and …