348 349
approximation see Nedelec elements
preconditioning 271
347
approximation see Raviart-Thomas elements
preconditioning 271
Affine mapping 371
anisotropic meshes 202 206 215 273
Average operator 134 139 140 151 208
basis functions Lagrangian 373
Block preconditioners 24 235 241 258
Carding inequality 313 364
Cauchy-Schwarz inequalities, strengthened 40
Coarse grid 59 90 219 274 289 314
Coloring 46
Condition number 395
condition number convergence of conjugate gradient 407
condition number of Schur complement 97 202
condition number of stiffness and mass matrix 390
Conjugate gradient 403
Conjugate residual 409
Convection-diffusion problems 311 326
Counting functions 134
counting functions for and 301
counting functions for elasticity 226
counting functions for scalar elliptic problems 134
counting functions for spectral elements 208
Curl see \Omega)$"/>
Darcy flows see porous media
Deville-Mund preconditioner 196
Direct methods 397
Dirichlet-Neumann 8 18 328
Discontinuous Galerkin 82 327
Divergence see
edge elements see Nedelec elements
eigenvalue problems 335
Eigenvalues 395
elasticity, linear approximation 375
elasticity, linear nearly incompressible 257 366 388
elasticity, linear preconditioning 217
elasticity, linear well-posedness 357
extensions continuous spaces 342
extensions discrete harmonic see harmonic extensions discrete
Factorizations 397
FETI 131
FETI DP see dual-primal
FETI dual-primal 160
FETI dual-primal acceptable edge path 172 229
FETI dual-primal analysis 175
FETI dual-primal for elasticity 227
FETI dual-primal three dimensions 167
FETI dual-primal two dimensions 161
FETI for and 304
FETI for convection-diffusion 329
FETI for Helmholtz 332
FETI for porous media 241
FETI for spectral elements 208
FETI for Stokes problems 241
FETI one-level 143
FETI one-level for elasticity 227
FETI one-level nonredundant Lagrange multipliers 150
FETI one-level redundant Lagrange multipliers 156
FETI two subdomains 2 241
Fictitious domain methods 233
Fill-in 398
finite elements spaces 372
finite elements triangulation see triangulation
floating subdomains 88
Fredholm alternative 364
Friedrichs inequalities 104 343
Galerkin approximations 371
Gauss-Lobatto meshes 194
Gauss-Lobatto points 377
gmres 15 407
Green's formulas 47 349 350
harmonic extensions comparison 264
harmonic extensions for and 290 295
harmonic extensions for elasticity 222
harmonic extensions for porous media 253
harmonic extensions for spectral elements 201
harmonic extensions for Stokes problems 264
harmonic extensions, discrete 96
Helmholtz equation 312 330
Helmholtz equation FETI-H 332
Helmholtz equation overlapping methods 331
Indefinite problems 362
indefinite problems algebraic 407
indefinite problems approximation 375
inexact solvers 36
Interface conditions see transmission conditions
interface, subdomain 88
interpolant projection 101
interpolant in 384
interpolant in 381
interpolant nodal into and from GLL meshes 195
interpolant quasi-interpolant 62
interpolant standard nodal 99 100 112 373
interpolant standard nodal for nonnested meshes 64
interpolation spaces 339 343
inverse inequalities 389
Jump operator 150
Korn inequalities 358
Lax-Milgram lemma 354 363
Lipschitz domain 337
Mass matrix 391
Maxwell’s equations 362
mesh see triangulation
Mixed methods see saddle point problems
mortar methods 233
Nedelec elements interpolant 384
Nedelec elements range and kernel of the curl 384
Nedelec elements three dimensions 383
| Nedelec elements two dimensions 382
Neumann-Dirichlet 15
Neumann-Neumann 10 16 131
Neumann-Neumann balancing 133 250 265 301
Neumann-Neumann for and 301
Neumann-Neumann for convection-diffusion 328
Neumann-Neumann for elasticity 225
Neumann-Neumann for porous media 250
Neumann-Neumann for spectral elements 208
Neumann-Neumann for Stokes problems 265
Neumann-Neumann two subdomains 10 241
Nonlinear problems 334
nonnested grids 64
optimal, method 9
Optimality 9
optimized interface conditions 333
overlap, definition/small/generous 56
overlapping metho ds 55
overlapping methods alternative coarse problems 75
overlapping methods analysis 67
overlapping methods for and 274
overlapping methods for elasticity 219
overlapping methods for Helmholtz 331
overlapping methods for nonsymmetric or indefinite problems 314
overlapping methods for porous media 255
overlapping methods for spectral elements 198
overlapping methods for Stokes problems 258
overlapping methods local solvers 56
overlapping methods numerical results 73
overlapping methods standard coarse spaces 59
partition of unity coarse spaces 84
partition of unity functions 57 105 204 295
Plane waves 333
Poincare inequalities 104 343
porous media, flows in approximation 389
porous media, flows in preconditioners 239
porous media, flows in well-posedness 367
positive definite problems 353
positive definite problems algebraic 395 403
positive definite problems approximation 374
Preconditioner 401 406 409
Projection see interpolant
quasi-optimal, method 18
quotient space arguments 60 346
Raviart-Thomas elements 380
Raviart-Thomas elements interpolant 381
Raviart-Thomas elements range and kernel of the divergence 384
Reference element 371
regularity results 369
Richardson method 399
Robin-Robin 328 329
saddle point problems approximation 386
saddle point problems well-posedness 364
Scalability 17
scalable methods 17
scaling arguments 60
Schur complement 5 94 201 244 251 263 290 397
Schur complement application 94
Schur complement application of the inverse 95
Schur complement condition number 97 202
Schur complement Uzawa algorithm 233 237
Schwarz methods additive 37
Schwarz methods alternating 21 27
Schwarz methods convergence theory 39
Schwarz methods definition 35
Schwarz methods hybrid 38 47 137
Schwarz methods implementation 52
Schwarz methods multiplicative 37
Schwarz methods restricted 75
Smoothed aggregation 81
Sobolev spaces definition 337
Sobolev spaces immersions 340
Sobolev spaces traces 341
Sobolev spacesof vector-valued functions 346
spectral elements 376
spectral elements approximations 378
spectral elements interpolant 195 378
spectral elements preconditioners 193
spectral elements spaces 376
Spectral radius 395
Spectrum see eigenvalues
Steepest descent 402
Steklov-Poincare operator 6
Stiffness matrix 390
Stokes problem finite element approximations 387
Stokes problem preconditioners 257
Stokes problem spectral element approximations 388
Stokes problem well-posedness 366
subdomain partitions nonoverlapping 88
subdomain partitions overlapping 56
substructuring methods for and 288
substructuring methods for linear elasticity 220
substructuring methods for nonsymmetric or indefinite problems 320 327 331 333
substructuring methods for porous media 241
substructuring methods for scalar problems 113 131
substructuring methods for spectral elements 200
substructuring methods for Stokes problems 261
substructuring methods generalities 87
trace operators continuous spaces 341
trace operators in 349 350
trace operators in 347
Transmission conditions 2 4 242 245 331 333
Triangulation 371
triangulation quasiuniform 372
triangulation shape-regular 372
Uzawa algorithm 233
Weighted average average operator
wire basket an extension from 222
wire basket definition 89
wire basket method for 308
wire basket method for elasticity 221
wire basket method for spectral elements 206
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