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Li R., Chen Z., Wu W. — Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Volume Methods
Li R., Chen Z., Wu W. — Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Volume Methods

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Название: Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Volume Methods

Авторы: Li R., Chen Z., Wu W.

Язык: en

Рубрика: Математика/Численные методы/Конечные элементы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 442

Добавлена в каталог: 25.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$P_K$-interpolation      16
$V_h$-interpolation      16
Affine mapping      17
Area coordinates      11 116
Averaging function      2
Bilinear forms      20 37
Bilinear forms, boundedness      27 28 37
Bilinear forms, coercive      22
Bilinear forms, positive definite      22 28 37 40
Bilinear forms, symmetric      22
Bilinear forms, V-elliptic      22
Boundary conditions, essential      47
Boundary conditions, natural      47
C-uniform      179
Characteristic direction      326
Coercive condition      22
Collocation methods      31
Continuous extension      21 35 39 41
Continuous function spaces, $C^m([a, b]; X)$      275
Continuous function spaces, $C^m(\Omega)$      1
Continuous function spaces, $C_0^m(\Omega)$      1
Continuous imbedding      20
Decomposition      10 114 131
Decomposition, quadrilateral      131
Decomposition, triangular      10 114
Differential equations, biharmonic      26 187
Differential equations, convection-diffusion      326 344
Differential equations, coupled sound-heat      394
Differential equations, electromagnetic field      367
Differential equations, first order hyperbolic      296
Differential equations, hyperbolic-parabolic      394
Differential equations, nonlinear elliptic      187 227 356
Differential equations, nonlinear parabolic      235 272
Differential equations, parabolic      235
Differential equations, planar elastic      361
Differential equations, Poisson      25
Differential equations, regularized long wave      399
Differential equations, second order elliptic      111
Differential equations, second order hyperbolic      287
Differential equations, second order ODE      45
Differential equations, Stokes      385
Differential equations, system of first order hyperbolic      307
Differential equations, three-dimensional Poisson      371
Differential equations, water pollution      373
Downwind value      299
Dual argument      37
Dual decompositions (grids)      52 55 63 75 115 132 140 154 369 370 387
Dual decompositions (grids), barycenter      115
Dual decompositions (grids), central      132
Dual decompositions (grids), circumcenter      115
Dual operator      32
Dual space      32
Elliptic projection      240
Error estimates      33 37 40 42
Error estimates in $H^0$ norm      88 90 167 303 304 350
Error estimates in $H^1$ norm      58 69 86 129 137 233 292 296 338
Error estimates in $H^2$ norm      106 214 226
Error estimates in $W^{0,\infty}$ norm      91 173
Extreme Value Theorem      338 342
Finite element space      9 10
Finite elements, Adini      220
Finite elements, Adini rectangular      15
Finite elements, Bogner — Fox — Schmidt      15
Finite elements, Hermite cubic      12
Finite elements, inverse property of      19
Finite elements, Lagrange bi-quadratic      14
Finite elements, Lagrange bilinear      13
Finite elements, Lagrange linear      11
Finite elements, Lagrange quadratic      11
Finite elements, Zienkiewicz      12 202 204 205
Finite volume method      317
Fundamental lemma of variational methods      3
Galerkin generalized solutions      21
Galerkin methods      30 31 35 47 48
Generalized difference methods      52 76 101 114 131
Generalized difference methods, backward Euler      245
Generalized difference methods, conservative      120
Generalized difference methods, Crank — Nicolson      245
Generalized difference methods, cubic element      72 154 261
Generalized difference methods, generalized upwind      296 309 332 344 356 378
Generalized difference methods, highly accurate generalized upwind      350
Generalized difference methods, linear element      53 119
Generalized difference methods, mass concentration      235 254
Generalized difference methods, mixed      190 197
Generalized difference methods, nonconforming      202 220 386
Generalized difference methods, quadratic element      61 139
Generalized Galerkin methods      38 43
Godunov scheme      317 320
Green’s formulas      23
Hierarchical basis methods      410
Interpolation operator      16
Interpolation operator $II^{\ast}_h$      58 67 118 157
Interpolation operator $II_h$      59 69 118
Interpolation weak estimates      94 96 98 174
Isolated waves      407
L-region      5
Lax — Friedrichs scheme      320
Least square method      31
Line segment $\bar{PQ}$      115
Mass conservation      343
Monotone scheme      323
Nonconforming method      113
Norms, $C^m([a,b];X)$      275
Norms, $L^p{(a,b);X)      275
Norms, (-m,p)      7
Norms, (m,p)      4
Norms, discrete      66 79 124 145 158
Norms, quotient      16
Norms, semi-      5
Numerical flux      320
Optimal stress points      93
Osher’s split technique of nonlinear functions      356
Petrov — Galerkin method      31
Positive definite condition      22
Projection methods      30
Projection operators      30 31 36
Quadratic functional      22
Quadratic functional, minimum of      22
Quasi-parallelogram      179
Quasi-parallelogram, condition      272
Quasi-uniform      19 54
Reference element      17 132
Regular family      17
Riesz, generalized solution      22
Riesz, representation theorem      20 28 36 39 41
Riesz, variational principle      23
Sobolev spaces      1 4
Sobolev spaces, $H^m(\Omega)$      4
Sobolev spaces, $H^m_0(\Omega)$      4
Sobolev spaces, $H^{-m}(\Omega)$      7
Sobolev spaces, $L^p(\Omega)$      1
Sobolev spaces, $L^p({a,b);X)$      275
Sobolev spaces, $W^{-m,p'}(\Omega)$      7
Sobolev spaces, $W^{m,p}(\Omega)$      4
Sobolev spaces, $W^{m,p}_0(\Omega)$      4
Sobolev spaces, interpolation in      15 43
Stable      85
Superconvergence      92—94 96 97 100 174 182
Theorems, average approximation      2
Theorems, Babuska      28
Theorems, equivalent norm      5
Theorems, imbedding      7 8
Theorems, inverse property      19
Theorems, Lax — Milgram      27
Theorems, trace      5
Trace      5 8
Trial and test spaces      39 41 53 61 73 114 131 139 154
Uniquely approximate-solvable      33
Upwind value      299
V-elliptic condition      22
Variational principles      22 204
Variational principles, Ciarlet — Raviart      187
Variational principles, generalized Galerkin      49 51
Variational principles, Hermann — Miyoshi      196
Variational principles, potential energy      23
Variational principles, Riesz      23
Variational principles, virtual work      22 47
Volume coordinates      368
Weak convergence      32 34
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