Titlebook: Numerical Models for Differential Problems; Alfio Quarteroni Textbook 20091st edition Springer-Verlag Milan 2009 Analysis.Numerical modell

mechanical

Domain decomposition methods,ry-value problem on a partition of the computational domain into subdomains. As such, it provides a very convenient framework for the solution of . or multiphysics problems, i.e. those that are governed by differential equations of different kinds in different subregions of the computational domain.

确定

Alfio QuarteroniAuthor faces here the basic concepts for the numerical modelling of partial differential equations.An outstanding reference work in this branch of applied mathematics.Includes supplementary material:

冷淡一切

欲望

Elements of functional analysis,In this chapter, we recall a number of concepts used extensively in this textbook: functional and bilinear forms, distributions, Sobolev spaces, L. spaces. For a more in-depth reading, the reader can refer to e.g. [Sa108],[Yos74], [Bre86], [LM68], [Ada75].

旋转一周

Elliptic equations,This chapter is devoted to the introduction of elliptic problems and to their weak formulation. Although our introduction is quite basic, the complete novice to functional analysis is invited to consult Chap. 2 before reading it.

Commentary

The Galerkin finite element method for elliptic problems,In this chapter, we describe the numerical solution of the elliptic boundary-value problems considered in Chap. 3 by introducing the Galerkin method. We then illustrate the finite element method as a particular case. The latter will be further developed in the following chapters.

freight

Substance-Abuse

The finite volume method,The . method is a very popular method for the space discretization of partial differential problems in conservation form. For an in-depth presentation of the method, we suggest the monographs [LeV02a] and [Wes01].

Entropion

割让

Finite elements and spectral methods for hyperbolic equations,In this chapter, we will illustrate how to apply Galerkin methods, and in particular the finite element method and the spectral one, to the spatial and/or temporal discretization of scalar hyperbolic equations. We will treat both the continuous as well as discontinuous finite element cases.