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Johnson C. — Numerical solution of partial differential equations by the finite element method
Johnson C. — Numerical solution of partial differential equations by the finite element method

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Название: Numerical solution of partial differential equations by the finite element method

Автор: Johnson C.

Аннотация:

This book gives an introduction to the finite element method as a general method for the numerical solution of partial differential equations in science and engineering. The finite element method has been developed over the last twenty years and is today a dominating technique in computational mathematics with important applications in many areas. The book gives the mathematical foundation of the method together with important numerical aspects but there is also a clear connection with applications and many examples from various fields are considered. A strong effort has been made to make the presentation of the mathematics as non-technical and easily accessible as possible, while still maintaining a mathematical framework stressing fundamenta! concepts as stability, regularity etc. All the basic linear partial differential equations are considered, i e, elliptic, parabolic and hyperbolic type problems, stationary as well as time-dependent problems. There is also one chapter on finite element methods for integral equations (boundary element methods) and an introduction to nonlinear problems The book contains unique recent developments of finite element techniques to parabolic problems including methods for automatic time step control, and in particular to hyperbolic problems with important applications to e g fluid mechanics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 275

Добавлена в каталог: 12.09.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^{0}(\bar{\Omega})$      67
$C^{1}(\bar{\Omega})$      67
$H^{1}(I)$      35
$H^{1}(\Omega)$      36
$H^{1}_{0}(I)$      35
$H^{1}_{0}(\Omega)$      36
$H^{2}_{0}(\Omega)$      59
$H^{k}(\Omega)$      58
$L_{2}(I)$      34
$L_{2}(\Omega)$      36
$L_{2}(\Omega)$-projection      99
$P_{r}(K)$      68 78
$Q_{1}(K)$      78
$Q_{2}(K)$      79
Adaptive methods      45 94
Artificial diffusion      181
assembly      32 47
Automatic time and space step control      158
Automatic time-step control      147
Babuska — Brezzi condition      234
Backward Euler      147 153
Backward substitution      113
Band matrix      114
Band width      114
Basis      68
Basis function      19 29
Beam      22
Bending moment      108
Biharmonic problem      59
Bilinear      78
Bilinear form      34
Boundary condition      14 64
Boundary element methods      12 214
Boundary layer      175
Boundary value problem      14 15
Box scheme      201
Burgers' equation      263
Cauchy sequence      34
Cauchy's inequality      24 34
Central difference      177
Characteristic curves      168
Characteristics      168
Chebyshev polynomial      134
Cholesky's method      114
Clamped      109
Classical artificial diffusion      173
Classical solution      37
Closed set      250
Compact      229
complete      34
Condition number      126 141
Conditionally stable      156
conjugate      131
Conjugate gradient method      124 131
Conservation of energy      15 61
Constitutive relation      102
Constrained minimization problem      250
continuous      50
Continuous functional      250
Convection-diffusion      166 168
Convection-diffusion problem      60
Convex functional      249
Convex minimization problem      248
Convex set      249
Corner singularity      93
Crank — Nicolson      147
Crank — Nicolson method      154
Curvature      108
Deflection      108
Deformation      102
Dense      114
Descent direction      124
Difference method      10 22 31
Direct method      112
Dirichlet condition      40
Discontinuous Galerkin method      147 157 167 173 189 261
Displacement      101
Displacement methods      66
Divergence theorem      26
Double layer potential      218
Dual space      98
Duality      97 151
Elastic bar      14
Elastic cord      15
Elastic plate      108
Elasticity problem      101
Elasto-plastic problem      254
Element degree of freedom      69
Element stiffness matrices      46
Element stiffness matrix      32
Energy norm      55
Equilibrium equation      14 102
Equilibrium method      66
Error estimate      42 52 54 84
Essential boundary condition      41
Euler equations      258
Explicit      156
Exterior Dirichlet problem      214
Fill-in      117
Finite element      79
Finite element method(FEM)      9
Forward Euler      155
Forward substitution      113
Fourier's law      15 61
Fredholm equation of the first kind      215 224
Fredholm equation of the second kind      215 227
Free boundary      109
Freely supported      109
Friedrichs' system      171
Friedrichs' systems      205
Frontal method      117
Functional      10
Fundamental solution      216
Galerkin methods      11 20
Gaussian elimination      112
Generalized conjugate gradient      257
Global degree of freedom      69
Gradient      27 124
Gradient method      124 255
Green's formula      26
Green's function      43
Heat conduction      15
hessian      124
Hilbert space      34
Hooke's law      14 102
Hyperbolic      168
IMPLICIT      153
Incomplete factorizations      137
Incompressible      106 258 262
Initial transient      148
Integral equation      215
Integral operator      216
Interpolant      24
Interpolation      84
Inverse estimate      141
Isoparametric      240
Iterative method      112
Jacobian      242
Korn's inequality      104
Krylov subspace      135
Lagrange type      239
Lax — Milgram Theorem      51
Lax — Wendroff      201
Layer      175
Leap-frog      201
Level curve      126
Line-search      125
Linear      34
linear combination      19
Linear form      34
Linear space      19
Load vector      20
Lower triangular      113
LU-factorization      112
Mass matrix      145 150
Minimal surface problem      252
Minimization algorithm      112 123
Minimization problem      10 15 50
Mixed finite element method      232 233
moment      108
Multi-grid      137
Natural boundary condition      41
Navier — Stokes equations      262
Nested dissection      120
Neumann condition      40
Neumann problem      40
Newmark method      213
Newtons method      256
nodes      29
Non-linear      61
Non-linear parabolic problem      257
Norm      24 34 55
Normal derivative      27
Normal moment      109
Normal stress      101
Numerical integration      245
Obstacle      251
Orthogonal      38
Parabolic problem      146
Perfectly plastic      253
Petrov — Galerkin method      187
Piecewise polynomial      11
Poisson equation      26
Poisson ratio      102 110
Polygonal domain      28
Positive definite      21
Preconditioning      136
Principle of minimum complementary energy      65
Principle of minimum potential energy      16
Principle of virtual work      16
Projection      39 55 197
Quadrature      245
Quasi-Newton methods      256
Quasi-uniform      141
Quasi-uniform mesh      45
Reduced problem      174
Reference triangle      143
Regularity      92
Riesz' representation theorem      51
Ritz — Galerkin method      11
Ritz' method      20
Robin boundary condition      64
Scalar product      24 34
Search direction      124
Second order hyperbolic problems      210
Semi-discrete      146
Seminorm      89
Shasta      201
Shear stress      101
Shock-capturing      186
Single layer potential      218
Singularities at corner      93
Skyline      116
Smoothing      228
Sobolev space      59
Software      48
Space-time elements      196 199
sparse      21
Stability estimate      51 54 148 185
Standard Galerkin      173 177
Steepest descent method      125
Step length      124
Stiff      146
Stiffness matrix      20
Stokes equations      106 232
Stream function      107 259
Streamline diffusion      167 173
Streamline diffusion method      182 260 261 263 264
Streamlines      168
Stress tensor      101
Support      29
symmetric      21 34
Symmetric hyperbolic system      171
Test function      16
Time discontinuous streamline diffusion      173
Tolerance      94
Total potential energy      16 27
Transversal force      109
Triangulation      28 44
Twisting moment      108 109
Unconditionally stable      156
Unconstrained minimization problem      250
Upper triangular      113
Upwind difference scheme      192
Upwind method      192 201
V-elliptic      50
Variable coefficient      61
Variational problem      10 15 51
Vorticity      259
Wave equation      205 208
Weak formulation      37
Weak solution      37
Weakly singular      215
Young modulus      102 110
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