1 Introduction to the equations of fluid dynamics and the finite element
1.1 General remarks and classification of fluid dynamics problems discussed in this book
1.2 The governing equations of fluid dynamics
1.3 Inviscid, incompressible flow
1.4 Incompressible (or nearly incompressible) flows
1.5 Numerical solutions: weak forms, weighted residual and finite element approximation
1.6 Concluding remarks
2 Convection dominated problems – finite element approximations to the convection–diffusion-reaction equation
2.2 The steady-state problem in one dimension
2.3 The steady-state problem in two (or three) dimensions
2.4 Steady state -- concluding remarks
2.5 Transients -- introductory remarks
2.6 Characteristic-based methods
2.7 Taylor--Galerkin procedures for scalar variables
2.8 Steady-state condition
2.9 Non-linear waves and shocks
2.10 Treatment of pure convection
2.11 Boundary conditions for convection--diffusion
2.12 Summary and concluding remarks
3 The characteristic-based split (CBS) algorithm. A general procedure for compressible and incompressible flow
3.2 Non-dimensional form of the governing equations
3.3 Characteristic-based split (CBS) algorithm
3.4 Explicit, semi-implicit and nearly implicit forms
3.5 Artificial compressibility and dual time stepping
3.6 ‘Circumvention’ of the Babu¡ska--Brezzi (BB) restrictions
3.7 A single-step version
It is very difficult to write a book which covers the entire finite element field. ..The authors have made a splendid attempt at a very difficult task. The books remain a tremendous bargain...and are an invaluable guide to the entire field of finite elements. If you are serious about working on finite elements you cannot do without this book.
- Mathematics Today, August 2001.
"...the publication of the first edition was an epoch making event...it is written by...the greatest theorist of the subject. If you are serious about finite elements, this is a book that you simply cannot afford to be without."
- International Journal of Numerical Methods in Engineering.
"..the pre-eminent reference work on finite element analysis."
- Applied Mechanical Review
"...a very good book...presentation is first class...will be of great assistance to all engineers and scientists interested in the method...a very commendable piece of work."
- Journal of the British Society for Strain Measurement