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 …

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

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

A Discontinuous Galerkin method is used for to the numerical solution of the time-domain
Maxwell equations on unstructured meshes. The method relies on the choice of local basis …

One approximates the entropy weak solution u of a nonlinear parabolic degenerate
equation u_t+\rmdiv(\mathbfqf(u))-Δϕ(u)=0 by a piecewise constant function u_\mathcalD …

Sympathetic cooling of two atomic isotopes is experimentally investigated. Using forced
evaporation of a bosonic 7 Li gas in a magnetic trap, a sample of 1.3× 10 5 6 Li fermions has …

We give a synthetic statement of Kružkov-type estimates for multi-dimensional scalar
conservation laws. We apply it to obtain various estimates for different approximation …

This paper is devoted to the study of an error estimate of the finite volume, approximation to
the solution u L∞(RN x R) of the equation ut+ div (V f (u))= 0, where v is a vector function …

We study here a finite volume scheme for a diffusion‐convection equation on an open
bounded set Ω of ℝ2, using a triangular mesh for the discretization of Ω. The 4‐point …

In this paper we shall derive a posteriori error estimates in the $ L^ 1$-norm for upwind finite
volume schemes for the discretization of nonlinear conservation laws on unstructured grids …