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| Bangerth W., Rannacher R. — Adaptive Finite Element Methods for Differential Equations |
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| Предметный указатель |
Adaptation strategy, error-balancing 35 47 50 63 187
Adaptation strategy, fixed error-reduction 48
Adaptation strategy, fixed rate 48 60 88 149 154
Adaptation strategy, mesh-optimization 48 58
Adjoint see "Dual"
Admissible state 102 105
Anisotropic mesh see "Mesh"
Aspect ratio 56
Backward Euler scheme 15 17 116
Bifurcation 75
Boundary approximation 35
Boundary condition, Dirichlet 37
Boundary condition, Neumann 37
Boundary condition, nonhomogeneous 37 148
Boundary condition, outflow 144
Boundary control 105 152
Boundary layer 55 90
Burgers equation 72 79 97 99 178
cG(1) method 24 124 128 168
control boundary 101
Control form 102 152
control variable 102
Convection-diffusion equation 88 99
Cost functional 101
Crank — Nicolson scheme 124
Curved boundary 35 148
Cylinder-flow problem 5 144
Defect correction 43 78 127
Defect of eigenvalue 82
Deviatoric part 130
dG(0) method 16 116 122 169
Diffusion-reaction equation 72 80
Domain of dependence 127
Drag coefficient 3 6 42 144
Drag coefficient, volume formula 145 160 189
Dual problem for eigenvalue problem 82 91
Dual problem for elasticity problem 130
Dual problem for evolution problem 115
Dual problem for heat equation 116
Dual problem for Hencky model 135
Dual problem for linear system 12
Dual problem for Navier — Stokes problem 147
Dual problem for nonlinear system 13
Dual problem for ODE system 17
Dual problem for parameter estimation 111
Dual problem for Poisson equation 27
Dual problem for stability problem 96
Dual problem for wave equation 125
Dual problem in space-time 164
Dual solution see "Dual problem"
Dual variable 103
Duality argument for linear system 12
Duality argument,  66
Duality argument, discrete 22
DWR method 3 11 25
Effectivity index 42 133
Eigenfunction see "Eigenvector"
Eigenvalue problem 11 81 99 112 157
Eigenvalue, critical 157 159
Eigenvalue, deficient 158
Eigenvalue, multiple 85 93 158
Eigenvector, dual 82 90
Eigenvector, generalized 158
Eigenvector, normalization 82 112
Eigenvector, primal 82 90
Elasticity 129
Elasto-plasticity 134
End-time error see "Error"
Energy form 130
Energy functional 129 134
Energy norm 29 130
Energy-norm error estimator for eigenvalue problem 88
Energy-norm error estimator for elasticity problem 131
Energy-norm error estimator for Hencky model 137
Energy-norm error estimator for Navier — Stokes problem 149
Energy-norm error estimator for ODE system 18
Energy-norm error estimator for optimization problem 106
Energy-norm error estimator for Poisson equation 29
Energy-norm error estimator for wave equation 126
Equilibration of indicators 50 62
Error estimator 41
Error estimator for eigenvalue 86
Error estimator for elasticity problem 131
Error estimator for heat equation 118
Error estimator for Hencky model 136
Error estimator for linear system 12
Error estimator for Navier — Stokes problem 148
Error estimator for nonlinear system 13
Error estimator for ODE system 18
Error estimator for optimization problem 106
Error estimator for Poisson equation 28
Error estimator for stability problem 98
Error estimator for wave equation 126
Error estimator in negative-norm 38
Error estimator of Zienkiewicz — Zhu 136
Error estimator, efficiency 45
Error estimator, global (for heat equation) 120
Error estimator, global (for ODE system) 20
Error expansion 68
Error representation for curved boundary 36
Error representation for drag minimization 154
Error representation for eigenvalue 84
Error representation for eigenvector 92
Error representation for elasticity problem 131
Error representation for evolution problem 115
Error representation for heat equation 117
Error representation for Hencky model 135
Error representation for higher-order element 37
Error representation for linear problem 71
Error representation for Navier — Stokes problem 147
Error representation for ODE system 18
Error representation for optimization problem 104
Error representation for parameter estimation 111
Error representation for Poisson equation 28 41
Error representation for stability problem 158
Error representation for stationary point 73
Error representation for variational equation 74
Error representation for wave equation 125
Error,  -norm 30 33 38 80 116
Error, dual 39 71
Error, end-time 17 19 120
Error, energy-norm 29 38 39 52
Error, equation 22
Error, global norm 25
Error, interpolation 119
Error, point-value 25 31 39 61
Error, primal 71
Error-balancing see "Adaptation strategy"
Euler equations 10
Euler — Lagrange Method 73
Euler — Lagrange system 73 103 153
Evolution problem 113
Finite difference method 15
Finite element space 27
Finite element, biquadratic 43 65
Finite element, discontinuous 16 116 164
Finite element, higher-order 37 44
Finite element, mixed 164
Finite element, non-conforming 36 164
Finite element, space-time 114
Finite volume method 165
| Fixed error-reduction see "Adaptation strategy"
fixed rate see "Adaptation strategy"
Flow reactor 9
Fredholm alternative 92
Galerkin approximation in space-time 114
Galerkin approximation of eigenvalue problem 82
Galerkin approximation of elasticity problem 130
Galerkin approximation of Hencky model 134
Galerkin approximation of Navier — Stokes problem 146
Galerkin approximation of ODE system 16
Galerkin approximation of optimization problem 103
Galerkin approximation of Poisson equation 26
Galerkin approximation of stability problem 96
Galerkin approximation of stationary points 73
Galerkin approximation of variational equations 72
Galerkin approximation of wave equation 124
Galerkin orthogonality 17 26 37 115 124 130 165
Green function 28 31 39 61 66
Gronwall lemma 16
Growth factor 16 21
Hanging node 27 46 60 113 124 175
Heat equation 115
Heat-driven cavity 7
Helmholtz equation 125
Hencky model 134
hp-method 164
Hydrodynamic stability see "Stability"
Hyperbolic problem 113 123
Implicit midpoint rule 24 128
Incompressibility 141
Inf-sup condition 141 142 146
Influence factor 28
Initial condition 114
Initial value problem 15
Interpolation constant 18 34 44
Interpolation,  -stable 68
Interpolation, anisotropic 57
Interpolation, biquadratic 52 53
Interpolation, error estimate 29 30
Interpolation, higher-order 34 38 43 66
Inverse relation 64
Jump operator 27
Korn inequality 130 188
Krylov-space method 78 164
Lagrangian functional 73 83 103 110 152
Lame — Navier equations 10 129
Lift coefficient 144
Local residual problem 44
Mach number 7
Mean normal flux 25 32 42
Mean normal stress 132
Mesh efficiency 54 89 91 94 109 138 150 151
Mesh optimization 49
Mesh width 27
Mesh, anisotropic 55 115 164
Mesh, Cartesian 56
Mesh, dual 53
Mesh, isotropic 51
Mesh, optimal 47 62
Mesh, primal 52
Mesh, quadrilateral 46
Mesh, quasi-uniform 64
Mesh, space-time 113
Mesh, tensor-product 55 58
Mesh-size function 48
Misfit functional 110
Model adaptivity 163
Multigrid method 78 85 105 164
Navier — Stokes problem 2 7 11 42 79 81 95 99 143
Newton method 78 105 108 135 142 146 164 187
Nusselt number 7
Observation boundary 102
ODE system 15
Optimality system see "Euler — Lagrange system"
Optimization problem 11 101
Output functional 27 30
Parabolic problem 113
Parameter estimation 10 110 163
Perturbation equation 95
Petrov — Galerkin method 24 124
Poincare inequality 26 121 174
Poisson equation 25 28 39 42 52 58 60 69
post-processing 42 52 54 105 118 148 155 162
Prandtl — Reuss model 141
Pressure variable 141
Primal variable 103
Pseudo-time stepping 128
Radiative transfer equation 10
Refinement indicator 3 41
Regularization of cost functional 102
Regularization of optimization problem 110
Regularization of output functional 31 32 42 51 69
Residual of a linear system 11
Residual of a nonlinear equation 13
Residual of eigenvalue problem 84
Residual of Euler — Lagrange system 153
Residual of Galerkin approximation 27
Residual of ODE system 18
Residual, cell 28
Residual, control 103
Residual, dual 71 74 75 79 103
Residual, edge 28
Residual, primal 71 74 75 103
Reynolds number 2 7 144
Ritz projection 26 67
Singular perturbation 55
Singularity, corner 2 107
Singularity, edge 55
Singularity, slit 90
Singularity, smoothness indicator 28
Singularity, stress 132
Sobolev inequality 174
Stability constant for -norm error 30
Stability constant for elasticity equations 131
Stability constant for energy-norm error 29
Stability constant for heat equation 118 120
Stability constant for Navier — Stokes problem 149
Stability constant for ODE system 18
Stability constant for parameter estimation 111
Stability constant, continuous 12
Stability constant, discrete 11 23
Stability problem 95 99 156
Stability, dynamic 99 154
Stability, hydrodynamic 11 95
Stability, linearized 95 99 157
Stability, nonlinear 157
Stabilization of dual problem 147
Stabilization of eigenvalue problem 158
Stabilization of incompressibility 141 146
Stabilization of mass conservation 146
Stabilization of pressure 141 146
Stabilization of transport 146
State variable 102
Stationary point 73 103 108
Step-size control 16 23
Stokes element 145
Super-approximation 67 175
Time-dependent problem 113
Truncation error 11 16 21
Variational crime 164
Variational inequality 134 142
Wave equation 10 123
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