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Li R., Chen Z., Wu W. — Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Volume Methods |
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Предметный указатель |
-interpolation 16
-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, 275
Continuous function spaces, 1
Continuous function spaces, 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 norm 88 90 167 303 304 350
Error estimates in norm 58 69 86 129 137 233 292 296 338
Error estimates in norm 106 214 226
Error estimates in 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 58 67 118 157
Interpolation operator 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 115
Mass conservation 343
Monotone scheme 323
Nonconforming method 113
Norms, 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, 4
Sobolev spaces, 4
Sobolev spaces, 7
Sobolev spaces, 1
Sobolev spaces, 275
Sobolev spaces, 7
Sobolev spaces, 4
Sobolev spaces, 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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