Approximation on a rectangular grid | with application to finite element methods and other problems

S. G. Mikhlin

ISBN 10: 9400995407 / ISBN 13: 9789400995406

Published by Springer Netherland, 2011

About this Item

Approximation on a rectangular grid | with application to finite element methods and other problems | S. G. Mikhlin | Taschenbuch | xi | Englisch | 2011 | Springer Netherland | EAN 9789400995406 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand.

Seller Inventory # 105625715

Bibliographic Details

• Title: Approximation on a rectangular grid | with application to finite element methods and other problems
• Publisher: Springer Netherland
• Publication Date: 2011
• Language: English
• ISBN 10: 9400995407
• ISBN 13: 9789400995406
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 229W x 152H x 14D millimeters 229 millimeters width by 152 millimeters height by 14 millimeters depth
• Weight: 354 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

The present monograph has points in common with two branches of analysis. One of them is the variational-difference method (the finite element method), the other is the constructive theory of functions. The starting point is the construction of special classes of coordinate functions for the variational-difference method. It is based on elementary transformations .of the independent variables of given "primitive" functions. After the construction of the coordinate functions, the next step is to approximate functions of a given class by linear combinations of the coordinate functions, and to derive in some appropriate norm an estimate of the error. Clearly, this is a problem closely connected with the constructive theory of functions. The monograph contains 11 chapters. Chapter I discusses Courant's basic idea which is central to the construction of variational-difference methods. One of Courant's examples, from which the notion of a primitive function follows naturally, is examined in some detail. The general definition of a primitive function and the method of construction for the corresponding coordinate functions are given and discussed. Chapters II-VI are more closely connected with the constructive theory of functions. The completeness of the coordinate systems defined in Chapter I are studied, as well as the order of approximation obtained through the use of linear combinations of these functions. Their completeness in Sobolev spaces are examined in Chapter II, while related orders of approximation are derived in Chapter III.