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Elasticity theory is a classical discipline. The mathematical
theory of elasticity in mechanics, especially the linearized
theory, is quite mature, and is one of the foundations of several
engineering sciences. In the last twenty years, there has been
significant progress in several areas closely related to this
classical field, this applies in particular to the following two
areas. First, progress has been made in numerical methods,
especially the development of the finite element method. The finite
element method, which was independently created and developed in
different ways by sci entists both in China and in the West, is a
kind of systematic and modern numerical method for solving partial
differential equations, especially el liptic equations. Experience
has shown that the finite element method is efficient enough to
solve problems in an extremely wide range of applica tions of
elastic mechanics. In particular, the finite element method is very
suitable for highly complicated problems. One of the authors (Feng)
of this book had the good fortune to participate in the work of
creating and establishing the theoretical basis of the finite
element method. He thought in the early sixties that the method
could be used to solve computational problems of solid mechanics by
computers. Later practice justified and still continues to justify
this point of view. The authors believe that it is now time to
include the finite element method as an important part of the
content of a textbook of modern elastic mechanics."
The need to predict, understand, and optimize complex physical and
c- mical processes occurring in and around the earth, such as
groundwater c- tamination, oil reservoir production, discovering
new oil reserves, and ocean hydrodynamics, has been increasingly
recognized. Despite their seemingly disparate natures, these
geoscience problems have many common mathe- tical and computational
characteristics. The techniques used to describe and study them are
applicable across a broad range of areas. The study of the above
problems through physical experiments, mat- matical theory, and
computational techniques requires interdisciplinary col- boration
between engineers, mathematicians, computational scientists, and
other researchers working in industry, government laboratories, and
univ- sities. By bringing together such researchers, meaningful
progress can be made in predicting, understanding, and optimizing
physical and chemical processes. The International Workshop on
Fluid Flow and Transport in Porous - dia was successfully held in
Beijing, China, August 2{6, 1999. The aim of this workshop was to
bring together applied mathematicians, computational scientists,
and engineers working actively in the mathematical and nume- cal
treatment of ?uid ?ow and transport in porous media. A broad range
of researchers presented papers and discussed both problems and
current, state-of-the-art techniques.
This book describes in detail the current, state-of-the-art numerical treatment and simulation of multiphase flows in porous media. The porous media considered range from ordinary to fractured and deformable media, the models treated from single-phase compressible flow to multiphase multicomponent flow with mass interchange, while the computational algorithms encompass everything from classical iterative solvers to modern multigrid and domain decomposition approaches. Addressing many problems originating from the applied geosciences, the book focuses on their common mathematical and computational aspects. It will serve as an excellent research reference for all geoscientists, mathematicians, physicists, and engineers who work in the mathematical modeling and numerical simulation of multiphase flows in porous media.
There has been rapid development in the area of adaptive
computation over the past decade. The International Conference on
Recent Advances in Adaptive Computation was held at Zhejiang
University (Hangzhou, China) to explore these new directions. The
conference brought together specialists to discuss modern theories
and practical applications of adaptive methods. This volume
contains articles reflecting the invited talks given by leading
mathematicians at the conference. It is suitable for graduate
students and researchers interested in methods of computation.
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