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| Axellson O., Barker V.A. — Finite Element Solution of Boundary Value Problems. Theory and Computation |
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| Ïðåäìåòíûé óêàçàòåëü |
 interpolant 170 215 224 230
 matrix 42
Adjoint operator (see Operator)
Adjoint problem (see Boundary value problem)
Admissible function 65 73 130
Affine variable transformation 172 174 178 190 208 219 235 237 247 250 291
Almost-every where property 103
Anisotropic body 94 199
Array, BONODE 168 180 198
Array, EDGE 168 180 195—196
Array, ELNODE 168 180 189 191 196
Array, G 180 185 194
Array, INTPT 180 192
Array, k 180 185—187
Array, NODECO 168 180 191 196
Array, PHI 181 192
Array, PHIX 181 192
Array, PHIY 181 192
Array, W 181 192
Aubin — Nitsche method 227—229 373
Back substitution 280 287
Band matrix 269—278 286 385
Band matrix, bandwidth 270
Band matrix, half-bandwidth 270 286
Band matrix, size of band 277 278
Band matrix, variable bandwidth 271 286—287 289
Barycentric coordinates 400
Basic two-level grid step 396
Basis functions (see Finite element basis functions)
Basis functions, complete set of 148
Basis functions, dimension-dependent 148—149
Basis functions, dimension-independent 148—149 151
Biharmonic equation 88
Bilinear form 106 118
Bilinear form, boundedness property 118
Bilinear form, coerciveness property 118
Bilinear form, symmetry property 106 118
Biquadratic polynomial 249
Block — SSOR preconditioning 337 408—412
Boundary condition, Dirichlet 83 95 143 233—234 327 338 373
Boundary condition, essential 74—80 82—83 87—88 90-91 112 120 168 185 204
Boundary condition, inhomogeneous 127—130
Boundary condition, mixed 84 129
Boundary condition, natural 74—80 82—84 87—88 90—92 95 112 120—121 168 185 203—204
Boundary condition, Neumann 83 95 334 336 338 358
Boundary condition, periodic 98
Boundary condition, third type (Robin) 84
Boundary value problem (see Boundary condition)
Boundary value problem in context of Lax-Milgram lemma 120—122
Boundary value problem, adjoint problem 121—122 228
Boundary value problem, classical solution of 102 121
Boundary value problem, definition of 64
Boundary value problem, fourth-order 71—73 85—89 95 171
Boundary value problem, generalized solution of 102 121 129—130 137 159
Boundary value problem, self-adjoint property 121
Boundary value problem, sources of 92—95
Boundary value problem, two-point 69—73 78 230
Boundary value problem, variational formulation of 69 72 107 113 115 135 182 228 245—246
Brachistochrone problem 96 98
Bramble — Hilbert lemma 219 221—223
Cauchy sequence 104 108—109 114 132
Cauchy — Schwarz inequality 5 104 108 120 123 131 138 216 342 397
Chebyshev iteration 395
Chebyshev polynomial 26 422—425
Cholesky factorization 284 290 295 298—299 315 317
Cholesky method (see Cholesky factorization)
Compact support 115 117
Complete polynomial 170
Completion of a set of admissible functions 101 107—113
Computational labor, conjugate gradient method (simple) 23—24 52 384 388—391
Computational labor, direct methods 286—287 302—303 385 388—391
Computational labor, multigrid methods 397 406
Computational labor, preconditioning by incomplete factorization 52 56 369—373 384 388
Computational labor, SSOR preconditioning 52 56 384 388—391
Computer programs that implement direct methods 307
Condensed matrix (see Superelement matrix)
Cone condition 222
Congruence transformation 284 288
Conjugate gradient method (simple) 18—28
Conjugate orthogonality 22
Conormal derivative 126
Consistency condition 125
Continuity condition of current flow 93
Convergence in the mean 104
Convex functional 58
Convex subset 57
Critical term 242—243
Cuthill — McKee algorithm 276
DATA ERROR 308 369 374 376—378 381
Data structure (see Storage scheme)
Data transfer 286—287 289 306
Defect-correction method 393—394
Deflection of a frame 205—206
Deflection of a plate 87—89
Deflection of abeam 77—78 135—136
Degree of freedom 171
Degree of graph node 276
Density of nonzero entries in matrix band 277—278
Descent direction 10
Diagonal scaling 56 59 238 317 376
Diagonally dominant matrix 42 203 337
Diffusion 94
Dirac delta function (see Symbolic function)
Direct method 279 (see also Cholesky factorization)
Directional derivative 5 66
Discontinuous coefficient 238 245—247 332 336 338 383 392
Discretization error 214—215 226—232 241 244 246 313 386 388 391 406
Discretization error,  norm of 227—229
Discretization error, maximum norm of 230—232
Discretization error, pointwise 231—232
Discretization error, Sobolev norm of 226—227
Double-precision accuracy 287 315 377 382
Dual space 131
Edge integral 194—198
Edge ratio 225—226 238 315
Effective spectral condition number 27
Eigenfunction 149 390 394
Eigenvalue cluster 28
Elemeni mass matrix 234
Elemeni mass matrix for model problems 259 260
Elemeni stiffness matrix (see Element matrix)
Element (of a finite element mesh) 165
Element (of a finite element mesh), degenerate 169
Element (of a finite element mesh), rectangular 177—179 225—226 249-250 362
Element (of a finite element mesh), Serendipity 250 402
Element (of a finite element mesh), standard 172 174 177 178 189 192—193 196 207 219 222 225 235 237
Element (of a finite element mesh), triangular 167 173—177 219 224 232 248—249 362 364
Element matrix 188—191 199—202 206 308 363 379
Element matrix for model problems 252—254 292 314—315 415—416
Element matrix, modified 294—295
Element vector 193—194 308 379
Element vector, modified 294—295
Elementary operation 279
Elliptic regularity 229 373 390
Energy inner product of two functions 108 121
Energy inner product of two vectors 13
Energy norm of a function 108 121
Energy norm of a vector 13
Envelope of a matrix 39 270—276 278 286 289 300
Equilibrium equation of heat flow 95
Equivalence class 102—103 112 170
Equivalent norms 114 119 121
Euclidean norm 3
Euler-Lagrange equation one space dimension 65—73 107
Euler-Lagrange equation, several dependent variables 90—92
Euler-Lagrange equation, three space dimensions 89—90
Euler-Lagrange equation, two space dimensions 80—89
Extension operator 395
Field equation 92—95
fill factor 304
| Fill-in 39 41 268 272 278 289 373
Fill-in matrix 370 373
Finite element basis functions, accuracy parameter k 170 173 176—177 179 209 217 224 226
Finite element basis functions, conforming 171
Finite element basis functions, global 168—171 175 179
Finite element basis functions, isoparametric 190 207—213
Finite element basis functions, local 171—173 175
Finite element basis functions, piecewise bilinear 177—179 200—203 272 277 301 327 337—338 340 360 401
Finite element basis functions, piecewise linear 173—176 200—203 215 232 277 305 314—315 327 330 337—340 344 360 364 371 379—380 388 393 404
Finite element basis functions, piecewise quadratic 176—177 277 290 301 364 393
Finite element basis functions, Serendipity 250 402
Finite element basis functions, singular isoparametric 244
Finite element basis functions, standard local 172—174 177—178 190 207 222 290
Finite element basis functions, support of 169
Finite element mesh 165—168 207 Node)
Finite element mesh, automatic generation 167—168
Finite element mesh, family 226 235
Finite element mesh, nonuniform 163 244 313 315
Finite element mesh, refinement of 167 202 204 244 367—368 374
Finite element mesh, regular family 226
Finite element space 168
Finite termination property 24
FLOP 52 286—287
Formal adjoint (see Operator)
Forward substitution 287
Fourier expansion 152 241
Friedrichs' second inequality 124
Friedrichs’ first inequality 123
Frontal method 305—307
Functional 2—3 65 67 71 81 85—90 94 105 119 Quadratic
Galerkin method, application to noncoercive problems 155—160
Galerkin method, error analysis 154
Galerkin method, formulation of 153—154
Garding’s inequality 159
Gauss — Seidel relaxation 395
Gaussian elimination 279—287
Gaussian elimination, pivoting in 281—282 311
Gaussian elimination, row-wise 282—287
Gaussian elimination, stability of 281 310—312
Gaussian elimination, symmetric 283—287
Gaussian factorization (see Gaussian elimination)
Generalized derivative 109—110 114 116—117 120
Generalized eigenvalue problem 365
Gradient error 227 391
Gradient function 99
Gradient vector 3 (see also Residual vector)
Gradient vector, recursive computation of 12 22 375
Green's function 136—139 230—232
Growth factor 42 44 311
Heaviside unit step function 133
Hessian matrix 4
Hilbert space (see Sobolev space)
Hilbert space, 115—116
Hilbert space, ![$L_{2}[a, b]$](/math_tex/c9e8f89bb0f262f794e6326c7b78332d82.gif) 102—105
Hilbert space, arbitrary 118
Hilbert space, completeness property 104 109 119 160
Homogeneous body 94
Householder matrix 287—289
III-conditioned system 232 282
Inhomogeneous body 94
Integration by parts 81
Interface condition 246
Interface corner 247
Internal boundary (see Material interface)
Interpolation in multigrid methods 395
Interpolation, error analysis of 215—226 246
Interpolation, Hermite 171 224—225
Interpolation, Lagrange 171 224
Inverse estimate 239
Inverse iteration 317
Isotropic body 94
Iterative refinement 38 315—316 369 391—392
Jacobian 189 219 225 235 237
L matrix 339
Law of Sines 259
Lax — Milgram lemma 118—130 135—136 145—146 150 152—155 160 245
Least squares 161
Lebesgue integral 102 115
Level structure (see Matrix graph)
Level surface 6
Line search 11
Linear functional 105 119 130 137 145 221
Linear functional, boundedness property 105 119
Linear functional, derivative of 133
Linear space 65 103
Local support 163 169
Machine precision parameter  310—311 314 374 384
Mass matrix 233—236
Mass matrix, spectral condition number of 236
Material interface 245—247
Matrix graph 272—276
Matrix graph, edge of 272
Matrix graph, level structure of 274—276
Matrix graph, node of 272
Matrix graph, rooted level structure of 274
Matrix graph, separator of 300
Matrix graph, set of paths of 339—340
Matrix graph, tree 322
Matrix partitioning method 297—300
Maximizer of a functional 3
Maximum angle condition 226
Maximum principle 257
Measure of a point set 103 122
Measure zero property 103 116
Method of steepest descent 9—15
Minimizer of a functional global 3 65
Minimizer of a functional local 3 65
Minimizer of a functional strong global 3 65
Minimizer of a functional strong local 3 65
Minimum angle condition 226
Minimum condition number 316
Mixed variational formulation 95 171
Multi-index notation for a partial derivative 116
Multigrid method 392—407
Navier’s equations 92
Neighborhood 3 65—66
Nested dissection 301—305
Nested dissection, ordering 304—305 387—388
Node (of a finite element mesh) 165
Node (of a finite element mesh), coordinates of 191
Node (of a finite element mesh), edge 165
Node (of a finite element mesh), global ordering of 167 186 268—269 281
Node (of a finite element mesh), interior 165
Node (of a finite element mesh), local ordering of 167 175 177—178 195
Node (of a finite element mesh), vertex 165
Numerical integration 191—193 213 232 254—255
Numerical integration, Gauss — Legendre formula 197 254
Numerical integration, integration point 191
Numerical integration, integration weight 191
Numerical stability (see Stability)
Oblique derivative 143
Ohm’s Law 94
One-way dissection ordering 300—301
Operator 107
Operator, adjoint of 122
Operator, formal adjoint of 122
Operator, linear property 107
Operator, self-adjoint (symmetric) property 121—122
Optimal error estimate 151
Optimal order process 404
Penalty method 143 161—162
Perturbation function (see Test function)
Perturbation of a linear system 308—310
Petrov — Galerkin method 154 262
Piecewise differentiable function 112
Piecewise polynomial 117 169
Pointwise convergence 104
Polar coordinates 241
Polar-coordinate element 244
Preconditioned conjugate gradient method (see Computational labor Preconditioning Preconditioning SSOR
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