| Description |
1 online resource (viii, 309 pages) : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
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text file |
| Series |
Studies in mathematics and its applications, 0168-2024 ; v. 30
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| Bibliography |
Includes commentary at chapter ends, bibliographical references (pages 275-302), and index. |
| Contents |
1. Elliptic boundary value problems and FEM ; 1.1 Elliptic boundary value problems -- 1.2 Ritz-Galerkin 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 Semi-discretization -- 2.3 Fractional powers -- 2.4 Full-discretization -- 2.5 Inhomogeneous equation -- 2.6 Higher accuracy -- 2.7 L[superscript]infinity [symbol] estimate -- 2.8 Hyperbolic equation |
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3. Evolution equations and FEM ; 3.1 Generation theories -- 3.2 A priori estimates -- 3.3 Semi-discretization -- 3.4 Full-discretization -- 3.5 Alternative approach -- 4. Other methods in time discretization ; 4.1 Rational approximation of semigroups -- 4.2 Multi-step 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) |
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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 (DD-NN) 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.
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Numerical analysis.
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Théorie des opérateurs.
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Analyse numérique.
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Numerical analysis.
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Numerical analysis. (OCoLC)fst01041273
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Operator theory. (OCoLC)fst01046419
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Operadores (teoria)
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Análise numérica.
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| Added Author |
Saito, Norikazu., author.
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Suzuki, Takashi., author.
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| Other Form: |
Print version: Fujita, Hiroshi, 1928- Operator theory and numerical methods. Amsterdam ; London : Elsevier, 2001 0444504745 9780444504746 (OCoLC)47063004 |
| ISBN |
9780444504746 |
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0444504745 |
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9780080538020 |
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0080538029 |
| Standard No. |
AU@ 000048130769 |
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AU@ 000062577590 |
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CHNEW 001006553 |
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DEBBG BV036962320 |
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DEBBG BV039830188 |
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DEBBG BV042317327 |
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DEBSZ 276900510 |
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DEBSZ 482355050 |
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NZ1 12433514 |
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NZ1 15192879 |
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DKDLA 820120-katalog:9910110519405765 |
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