Description 
1 online resource (viii, 309 pages) : illustrations 

text txt rdacontent 

computer c rdamedia 

online resource cr rdacarrier 

text file 
Series 
Studies in mathematics and its applications, 01682024 ; v. 30

Bibliography 
Includes commentary at chapter ends, bibliographical references (pages 275302), and index. 
Contents 
1. Elliptic boundary value problems and FEM ; 1.1 Elliptic boundary value problems  1.2 RitzGalerkin method  1.3 Finite element method (FEM)  1.4 Inverse assumption  1.5 L[superscript]infinity [symbol] estimate  1.6 L[superscript]p estimate  1.7 Asymptotic expansion  2. Semigroup theory and FEM ; 2.1 Evolutionary problems  2.2 Semidiscretization  2.3 Fractional powers  2.4 Fulldiscretization  2.5 Inhomogeneous equation  2.6 Higher accuracy  2.7 L[superscript]infinity [symbol] estimate  2.8 Hyperbolic equation 

3. Evolution equations and FEM ; 3.1 Generation theories  3.2 A priori estimates  3.3 Semidiscretization  3.4 Fulldiscretization  3.5 Alternative approach  4. Other methods in time discretization ; 4.1 Rational approximation of semigroups  4.2 Multistep method  4.3 Product formula  5. Other methods in space discretization ; 5.1 Lumping of mass  5.2 Upwind finite elements  5.3 Mixed finite elements  5.4 Boundary element method (BEM)  5.5 Charge simulation method (CSM) 

6. Nonlinear problems ; 6.1 Semilinear elliptic equations  6.2 Semilinear parabolic equations  6.3 Degenerate parabolic equations  7. Domain decomposition method ; 7.1 Dirichlet to Neumann (DN) map  7.2 Dirichlet to Neumann (DN) iteration  7.3 Dirichlet² to Neumann² (DDNN) iteration  7.4 Robin to Robin (RR) iteration  7.5 Exterior problem  7.6 The Stokes system. 
Summary 
Recent developments in numerical computations are amazing. A lot of huge projects in applied and theoretical sciences are becoming successful by them, while similar things are happening even in the level of personal computers. Under such a situation, theoretical studies on numerical schemes are fruitful and highly needed. The purpose of the present book is to provide some of them, particularly for schemes to solve partial differential equations. In 1991, we published an article on the finite element method applied to evolutionary problems from Elsevier Publishers (Fujita and Suzuki [148]). This book follows basically that way of description. We study various schemes from the operator theoretical point of view. Many parts are devoted to the finite element method, of which history is described in Oden [306]. We deal with elliptic and then time dependent problems in use of the semigroup theory and so forth. Some other schemes and problems are also discussed, with the later development taken also into account. We are led to believe that any scheme used practically has significant and tight structures mathematically and the converse is also true. 
Note 
Print version record. 
Subject 
Operator theory.


Numerical analysis.


Théorie des opérateurs.


Analyse numérique.


Numerical analysis.


Numerical analysis. (OCoLC)fst01041273


Operator theory. (OCoLC)fst01046419


Operadores (teoria)


Análise numérica.

Added Author 
Saito, Norikazu., author.


Suzuki, Takashi., author.

Other Form: 
Print version: Fujita, Hiroshi, 1928 Operator theory and numerical methods. Amsterdam ; London : Elsevier, 2001 0444504745 9780444504746 (OCoLC)47063004 
ISBN 
9780444504746 

0444504745 

9780080538020 

0080538029 
Standard No. 
AU@ 000048130769 

AU@ 000062577590 

CHNEW 001006553 

DEBBG BV036962320 

DEBBG BV039830188 

DEBBG BV042317327 

DEBSZ 276900510 

DEBSZ 482355050 

NZ1 12433514 

NZ1 15192879 

DKDLA 820120katalog:9910110519405765 
