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1.

図書

図書
Edward Angel, Richard Bellman
出版情報: New York : Academic Press, 1972  xi, 204 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 88
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2.

図書

図書
William F. Ames
出版情報: New York : Academic Press, 1977  xiv, 365 p. ; 24 cm
シリーズ名: Computer science and applied mathematics
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目次情報: 続きを見る
Fundamentals
Parabolic Equations
Elliptic Equations
Hyperbolic Equations
Special Topics
Author Index
Subject Index
Fundamentals
Parabolic Equations
Elliptic Equations
3.

図書

図書
by M. Š. Birman and M. Z. Solomjak ; [translated by F. A. Cezus ; edited by Lev J. Leifman]
出版情報: Providence, R.I. : American Mathematical Society, 1980  viii, 132p, ; 26cm
シリーズ名: American Mathematical Society translations ; ser. 2, v. 114
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4.

図書

図書
Liviu Gr. Ixaru
出版情報: Bucuresti, Romania : Editura Academiei , Dordrecht : D. Reidel, c1984  xxi, 337 p. ; 23 cm
シリーズ名: Mathematics and its applications ; East European series
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5.

図書

図書
Theodor Meis, Ulrich Marcowitz ; [translated by Peter R. Wadsack]
出版情報: New York : Springer-Verlag, c1981  viii, 541 p. ; 24 cm
シリーズ名: Applied mathematical sciences ; v. 32
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6.

図書

図書
George F. Carrier, Carl E. Pearson
出版情報: New York : Academic Press, 1976  xi, 320 p. ; 24 cm
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7.

図書

図書
C.A.J. Fletcher
出版情報: New York : Springer-Verlag, c1984  xi, 309 p. ; 25 cm
シリーズ名: Springer series in computational physics
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8.

図書

図書
Jacques-Louis Lions
出版情報: [Paris] : Gauthier-Villars, c1985  xxiv, 552 p. ; 25 cm
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9.

図書

図書
G. L. Lamb, Jr
出版情報: New York : Wiley, c1980  xii, 289 p. ; 24 cm
シリーズ名: Pure and applied mathematics
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10.

図書

図書
Ronghua Li, Zhongying Chen, Wei Wu
出版情報: New York : Marcel Dekker, c2000  xv, 442 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 226
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目次情報: 続きを見る
Preface
Preliminaries / 1:
Sobolev Spaces / 1.1:
Smooth approximations. Fundamental lemma of variational methods / 1.1.1:
Generalized derivatives and Sobolev spaces / 1.1.2:
Imbedding and trace theorems / 1.1.3:
Finite element spaces / 1.1.4:
Interpolation error estimates in Sobolev spaces / 1.1.5:
Variational Problems and Their Approximations / 1.2:
Abstract variational form / 1.2.1:
Green's formulas and variational problems / 1.2.2:
Well-posedness of variational problems / 1.2.3:
Approximation methods. A necessary and sufficient condition for approximate-solvability / 1.2.4:
Galerkin methods / 1.2.5:
Generalized Galerkin methods / 1.2.6:
Bibliography and Comments
Two Point Boundary Value Problems / 2:
Basic Ideas of the Generalized Difference Method / 2.1:
A variational form / 2.1.1:
Generalized Galerkin variational principles / 2.1.2:
Generalized difference methods / 2.1.4:
Linear Element Difference Schemes / 2.2:
Trial and test function spaces / 2.2.1:
Difference equations / 2.2.2:
Convergence estimates / 2.2.3:
Quadratic Element Difference Schemes / 2.3:
Trial and test spaces / 2.3.1:
Convergence order estimates / 2.3.2:
Cubic Element Difference Schemes / 2.4:
Some lemmas / 2.4.1:
Existence, uniqueness and stability / 2.4.4:
Numerical examples / 2.4.5:
Estimates in L[superscript 2] and Maximum Norms / 2.5:
L[superscript 2]-estimates / 2.5.1:
Maximum norm estimates / 2.5.2:
Superconvergence / 2.6:
Optimal stress points / 2.6.1:
Superconvergence for linear element difference schemes / 2.6.2:
Superconvergence for cubic element difference schemes / 2.6.3:
Generalized Difference Methods for a Fourth Order Equation / 2.7:
Generalized difference equations / 2.7.1:
Positive definiteness of a(u[subscript h], II*[subscript h] u[subscript h]) / 2.7.2:
Second Order Elliptic Equations / 2.7.3:
Introduction / 3.1:
Generalized Difference Methods on Triangular Meshes / 3.2:
Generalized difference equation / 3.2.1:
a priori estimates / 3.2.3:
Error estimates / 3.2.4:
Generalized Difference Methods on Quadrilateral Meshes / 3.3:
Numerical example / 3.3.1:
L[superscript 2] and Maximum Norm Estimates / 3.5:
L[superscript 2] estimates / 3.6.1:
A maximum estimate and some remarks / 3.6.2:
Superconvergences / 3.7:
Weak estimate of interpolations / 3.7.1:
Superconvergence estimates / 3.7.2:
Fourth Order and Nonlinear Elliptic Equations / 4:
Mixed Generalized Difference Methods Based on Ciarlet-Raviart Variational Principle / 4.1:
Mixed generalized difference equations / 4.1.1:
Mixed Generalized Difference Methods Based on Hermann-Miyoshi Variational Principle / 4.1.2:
Numerical experiments / 4.2.1:
Nonconforming Generalized Difference Method Based on Zienkiewicz Elements / 4.3:
Variational principle / 4.3.1:
Generalized difference schemes based on Zienkiewicz elements / 4.3.2:
Error analyses / 4.3.3:
Numerical experiment / 4.3.4:
Nonconforming Generalized Difference Methods Based on Adini Elements / 4.4:
Generalized difference scheme / 4.4.1:
Error estimate / 4.4.2:
Second Order Nonlinear Elliptic Equations / 4.4.3:
Parabolic Equations / 4.5.1:
Semi-discrete Generalized Difference Schemes / 5.1:
Problem and schemes / 5.1.1:
L[superscript 2]-error estimate / 5.1.2:
H[superscript 1]-error estimate / 5.1.4:
Fully-discrete Generalized Difference Schemes / 5.2:
Fully-discrete schemes / 5.2.1:
Error estimates for backward Euler generalized difference schemes / 5.2.2:
Error estimates for Crank-Nicolson generalized difference schemes / 5.2.3:
Mass Concentration Methods / 5.3:
Construction of schemes / 5.3.1:
Error estimates for semi-discrete schemes / 5.3.2:
Error estimates for fully-discrete schemes / 5.3.3:
High Order Element Difference Schemes / 5.4:
Cubic element difference schemes for one-dimensional parabolic equations / 5.4.1:
Quadratic element difference schemes for two-dimensional parabolic equations / 5.4.2:
Generalized Difference Methods for Nonlinear Parabolic Equations / 5.5:
Hyperbolic Equations / 5.5.1:
Generalized Difference Methods for Second Order Hyperbolic Equations / 6.1:
Semi-discrete generalized difference scheme / 6.1.1:
Fully-discrete generalized difference scheme / 6.1.2:
Generalized Upwind Schemes for First Order Hyperbolic Equations / 6.2:
Generalized upwind schemes / 6.2.1:
Semi-discrete error estimates / 6.2.2:
Fully-discrete error estimates / 6.2.3:
Generalized Upwind Schemes for First Order Hyperbolic Systems / 6.3:
Integral forms / 6.3.1:
Generalized upwind difference schemes / 6.3.2:
Estimation of a bilinear form / 6.3.3:
Some practical difference schemes / 6.3.4:
A numerical example / 6.3.5:
Finite Volume Methods for Nonlinear Conservative Hyperbolic Equations / 6.4:
Convection-Dominated Diffusion Problems / 7:
One-Dimensional Characteristic Difference Schemes / 7.1:
Difference methods based on algebraic interpolations / 7.1.1:
Upwind difference schemes / 7.1.2:
Generalized Upwind Difference Schemes for Steady-state Problems / 7.2:
Construction of the difference schemes / 7.2.1:
Convergence and error estimate / 7.2.2:
Extreme value theorem and uniform convergence / 7.2.3:
Mass conservation / 7.2.4:
Generalized Upwind Difference Schemes for Nonsteady-state Problems / 7.3:
Construction of difference schemes / 7.3.1:
Highly Accurate Generalized Upwind Schemes / 7.3.2:
Upwind Schemes for Nonlinear Convection Problems / 7.4.1:
Applications / 8:
Planar Elastic Problems / 8.1:
Displacement methods / 8.1.1:
Mixed methods / 8.1.2:
Computation of Electromagnetic Fields / 8.2:
Numerical Simulation of Underground Water Pollution / 8.3:
Upwind weighted multi-element balancing method / 8.3.1:
Stokes Equation / 8.4:
Nonconforming generalized difference method / 8.4.1:
Coupled Sound-Heat Problems / 8.4.2:
Regularized Long Wave Equations / 8.6:
Semi-discrete generalized difference schemes / 8.6.1:
Fully-discrete generalized difference schemes / 8.6.2:
Hierarchical Basis Methods / 8.6.3:
Hierarchical Basis / 8.7.1:
Application to difference equations / 8.7.2:
Iteration methods / 8.7.3:
Bibliography / 8.7.4:
Index
Preface
Preliminaries / 1:
Sobolev Spaces / 1.1:
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