This book is written primarily for Earth scientists faced with problems in thermo mechanics such as the flow and evolution of ice-sheets, convection currents in the mantle, isostatic rebound, folding of strata or collapse of cavities in salt domes. Failure, faults, seismic waves and all processes involving inertial terms will not be dealt with. In general such scientists (graduate students beginning a Ph. D. for instance) have too small a background'in continuum mechanics and in numerical computation to model conveniently these problems, which are not elementary at all. Most of them are not linear, and therefore seldom dealt with in treatises. If the study of reality were clearly cut into two successive steps: first to make a physical model, setting up a well-posed problem in thermo-mechanics, and second to solve it, the obvious solution would be to find a specialist in computational mechanics who could spend enough time on a problem which, although maybe crucial for on-going fundamental research, has little practical interest in general, and cannot be considered properly as a noteworthy progress in Mechanics. But this is not the way Science develops. There is a continuous dialectic between the building up of a model and its mathematical treatment. The model should be simple enough to be tractable, but not oversimplified. Its sensitivity to the different components it is made of should be investigated, and more thought is needed when the results contradict hard facts.

Zusammenfassung
` ... useful addition to the library of the researcher working on either glaciology or mantle convection. '
Pageoph, Vol.127,No.4.1988

Inhalt
1 Numerical simulation of very slow flows: an overview.- 2 Diffusion and advection of heat with a single space variable.- 3 Rotation and strain. Invariants of stress and of strain rates.- 4 Microscopic processes of creep.- 5 Viscosity as a model for rocks creeping at high temperature.- 6 Stokes' problems solved with Fourier transforms: isostatic rebound, glacier sliding.- 7 Open flow in a cylindrical channel of a power-law viscous fluid, and application to temperate valley glaciers.- 8 Coupled velocity and temperature fields: the ice-sheet problem.- 9 Thermal convection in an isoviscous layer and in the Earth's mantle.- 10 Computation of very slow flows by the finite-difference method.- 11 Elasto-statics.- 12 Plates and layered media.- 13 Variational theorems, and the Finite Element Method.- 14 The rigid plastic model.- 15 Viscoelasticity and transient creep.- 16 Homogenization, and the transversely isotropic power-law viscous body.- Appendix I Some important numerical methods.- Appendix II Vector analysis.- Appendix III Cylindrical and spherical coordinates.- Appendix IV Fourier and Fourier-Bessel transforms.- Appendix V Spherical harmonics and the gravity field.- Name index.