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Bangerth W., Rannacher R. — Adaptive Finite Element Methods for Differential Equations
Bangerth W., Rannacher R. — Adaptive Finite Element Methods for Differential Equations

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Название: Adaptive Finite Element Methods for Differential Equations

Авторы: Bangerth W., Rannacher R.

Аннотация:

Text compiled from the material presented by the second author in a lecture series at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self-adaptivity' in the numerical solution of differential equations are discussed, with emphasis on Galerkin finite element models.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 2003

Количество страниц: 207

Добавлена в каталог: 21.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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, $L^{\infty}-L^{1}$      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, $L^{2}$-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, $H^{1}$-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 $L^{2}$-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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