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Axellson O., Barker V.A. Ч Finite Element Solution of Boundary Value Problems. Theory and Computation
Axellson O., Barker V.A. Ч Finite Element Solution of Boundary Value Problems. Theory and Computation

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Ќазвание: Finite Element Solution of Boundary Value Problems. Theory and Computation

јвторы: Axellson O., Barker V.A.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2001

 оличество страниц: 432

ƒобавлена в каталог: 31.01.2010

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$V_{M}$ interpolant      170 215 224 230
$\hat{M}$ 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 195Ч196
Array, ELNODE      168 180 189 191 196
Array, G      180 185 194
Array, INTPT      180 192
Array, k      180 185Ч187
Array, NODECO      168 180 191 196
Array, PHI      181 192
Array, PHIX      181 192
Array, PHIY      181 192
Array, W      181 192
Aubin Ч Nitsche method      227Ч229 373
Back substitution      280 287
Band matrix      269Ч278 286 385
Band matrix, bandwidth      270
Band matrix, half-bandwidth      270 286
Band matrix, size of band      277 278
Band matrix, variable bandwidth      271 286Ч287 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      148Ч149
Basis functions, dimension-independent      148Ч149 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 Ч SSOR preconditioning      337 408Ч412
Boundary condition, Dirichlet      83 95 143 233Ч234 327 338 373
Boundary condition, essential      74Ч80 82Ч83 87Ч88 90-91 112 120 168 185 204
Boundary condition, inhomogeneous      127Ч130
Boundary condition, mixed      84 129
Boundary condition, natural      74Ч80 82Ч84 87Ч88 90Ч92 95 112 120Ч121 168 185 203Ч204
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      120Ч122
Boundary value problem, adjoint problem      121Ч122 228
Boundary value problem, classical solution of      102 121
Boundary value problem, definition of      64
Boundary value problem, fourth-order      71Ч73 85Ч89 95 171
Boundary value problem, generalized solution of      102 121 129Ч130 137 159
Boundary value problem, self-adjoint property      121
Boundary value problem, sources of      92Ч95
Boundary value problem, two-point      69Ч73 78 230
Boundary value problem, variational formulation of      69 72 107 113 115 135 182 228 245Ч246
Brachistochrone problem      96 98
Bramble Ч Hilbert lemma      219 221Ч223
Cauchy sequence      104 108Ч109 114 132
Cauchy Ч Schwarz inequality      5 104 108 120 123 131 138 216 342 397
Chebyshev iteration      395
Chebyshev polynomial      26 422Ч425
Cholesky factorization      284 290 295 298Ч299 315 317
Cholesky method      (see Cholesky factorization)
Compact support      115 117
Complete polynomial      170
Completion of a set of admissible functions      101 107Ч113
Computational labor, conjugate gradient method (simple)      23Ч24 52 384 388Ч391
Computational labor, direct methods      286Ч287 302Ч303 385 388Ч391
Computational labor, multigrid methods      397 406
Computational labor, preconditioning by incomplete factorization      52 56 369Ч373 384 388
Computational labor, SSOR preconditioning      52 56 384 388Ч391
Computer programs that implement direct methods      307
Condensed matrix      (see Superelement matrix)
Cone condition      222
Congruence transformation      284 288
Conjugate gradient method (simple)      18Ч28
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      242Ч243
Cuthill Ч McKee algorithm      276
DATA ERROR      308 369 374 376Ч378 381
Data structure      (see Storage scheme)
Data transfer      286Ч287 289 306
Defect-correction method      393Ч394
Deflection of a frame      205Ч206
Deflection of a plate      87Ч89
Deflection of abeam      77Ч78 135Ч136
Degree of freedom      171
Degree of graph node      276
Density of nonzero entries in matrix band      277Ч278
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 245Ч247 332 336 338 383 392
Discretization error      214Ч215 226Ч232 241 244 246 313 386 388 391 406
Discretization error, $L_{2}(\Omega)$ norm of      227Ч229
Discretization error, maximum norm of      230Ч232
Discretization error, pointwise      231Ч232
Discretization error, Sobolev norm of      226Ч227
Double-precision accuracy      287 315 377 382
Dual space      131
Edge integral      194Ч198
Edge ratio      225Ч226 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      177Ч179 225Ч226 249-250 362
Element (of a finite element mesh), Serendipity      250 402
Element (of a finite element mesh), standard      172 174 177 178 189 192Ч193 196 207 219 222 225 235 237
Element (of a finite element mesh), triangular      167 173Ч177 219 224 232 248Ч249 362 364
Element matrix      188Ч191 199Ч202 206 308 363 379
Element matrix for model problems      252Ч254 292 314Ч315 415Ч416
Element matrix, modified      294Ч295
Element vector      193Ч194 308 379
Element vector, modified      294Ч295
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 270Ч276 278 286 289 300
Equilibrium equation of heat flow      95
Equivalence class      102Ч103 112 170
Equivalent norms      114 119 121
Euclidean norm      3
Euler-Lagrange equation one space dimension      65Ч73 107
Euler-Lagrange equation, several dependent variables      90Ч92
Euler-Lagrange equation, three space dimensions      89Ч90
Euler-Lagrange equation, two space dimensions      80Ч89
Extension operator      395
Field equation      92Ч95
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 176Ч177 179 209 217 224 226
Finite element basis functions, conforming      171
Finite element basis functions, global      168Ч171 175 179
Finite element basis functions, isoparametric      190 207Ч213
Finite element basis functions, local      171Ч173 175
Finite element basis functions, piecewise bilinear      177Ч179 200Ч203 272 277 301 327 337Ч338 340 360 401
Finite element basis functions, piecewise linear      173Ч176 200Ч203 215 232 277 305 314Ч315 327 330 337Ч340 344 360 364 371 379Ч380 388 393 404
Finite element basis functions, piecewise quadratic      176Ч177 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      172Ч174 177Ч178 190 207 222 290
Finite element basis functions, support of      169
Finite element mesh      165Ч168 207 Node)
Finite element mesh, automatic generation      167Ч168
Finite element mesh, family      226 235
Finite element mesh, nonuniform      163 244 313 315
Finite element mesh, refinement of      167 202 204 244 367Ч368 374
Finite element mesh, regular family      226
Finite element space      168
Finite termination property      24
FLOP      52 286Ч287
Formal adjoint      (see Operator)
Forward substitution      287
Fourier expansion      152 241
Friedrichs' second inequality      124
FriedrichsТ first inequality      123
Frontal method      305Ч307
Functional      2Ч3 65 67 71 81 85Ч90 94 105 119 Quadratic
Galerkin method, application to noncoercive problems      155Ч160
Galerkin method, error analysis      154
Galerkin method, formulation of      153Ч154
GardingТs inequality      159
Gauss Ч Seidel relaxation      395
Gaussian elimination      279Ч287
Gaussian elimination, pivoting in      281Ч282 311
Gaussian elimination, row-wise      282Ч287
Gaussian elimination, stability of      281 310Ч312
Gaussian elimination, symmetric      283Ч287
Gaussian factorization      (see Gaussian elimination)
Generalized derivative      109Ч110 114 116Ч117 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      136Ч139 230Ч232
Growth factor      42 44 311
Heaviside unit step function      133
Hessian matrix      4
Hilbert space      (see Sobolev space)
Hilbert space, $L_{2}(\Omega)$      115Ч116
Hilbert space, $L_{2}[a, b]$      102Ч105
Hilbert space, arbitrary      118
Hilbert space, completeness property      104 109 119 160
Homogeneous body      94
Householder matrix      287Ч289
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      215Ч226 246
Interpolation, Hermite      171 224Ч225
Interpolation, Lagrange      171 224
Inverse estimate      239
Inverse iteration      317
Isotropic body      94
Iterative refinement      38 315Ч316 369 391Ч392
Jacobian      189 219 225 235 237
L matrix      339
Law of Sines      259
Lax Ч Milgram lemma      118Ч130 135Ч136 145Ч146 150 152Ч155 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 $\varepsilon_{M}$      310Ч311 314 374 384
Mass matrix      233Ч236
Mass matrix, spectral condition number of      236
Material interface      245Ч247
Matrix graph      272Ч276
Matrix graph, edge of      272
Matrix graph, level structure of      274Ч276
Matrix graph, node of      272
Matrix graph, rooted level structure of      274
Matrix graph, separator of      300
Matrix graph, set of paths of      339Ч340
Matrix graph, tree      322
Matrix partitioning method      297Ч300
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      9Ч15
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      392Ч407
NavierТs equations      92
Neighborhood      3 65Ч66
Nested dissection      301Ч305
Nested dissection, ordering      304Ч305 387Ч388
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 268Ч269 281
Node (of a finite element mesh), interior      165
Node (of a finite element mesh), local ordering of      167 175 177Ч178 195
Node (of a finite element mesh), vertex      165
Numerical integration      191Ч193 213 232 254Ч255
Numerical integration, Gauss Ч Legendre formula      197 254
Numerical integration, integration point      191
Numerical integration, integration weight      191
Numerical stability      (see Stability)
Oblique derivative      143
OhmТs Law      94
One-way dissection ordering      300Ч301
Operator      107
Operator, adjoint of      122
Operator, formal adjoint of      122
Operator, linear property      107
Operator, self-adjoint (symmetric) property      121Ч122
Optimal error estimate      151
Optimal order process      404
Penalty method      143 161Ч162
Perturbation function      (see Test function)
Perturbation of a linear system      308Ч310
Petrov Ч 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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