Langtangen H.P. Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

2nd Edition. — Springer-Verlag, Berlin, Heidelberg, 2003. — 882 p. — (Texts in Computational Science and Engineering 1) — ISBN: 9783642628115During the last decades there has been a tremendous advancement of computer hardware, numerical algorithms, and scientific software. Engineers and scientists are now equipped with tools that make it possible to explore real world applications of high complexity by means of mathematical models and computer simulation. Experimentation based on numerical simulation has become fundamental in engineering and many of the traditional sciences. A common feature of mathematical models in physics, geology, astrophysics, mechanics, geophysics, as well as in most engineering disciplines, is the appearance of systems of partial differential equations (PDEs). This text aims at equipping the reader with tools and skills for formulating solution methods for PDEs and producing associated running code.Getting Started
Introduction to Finite Element Discretization
Programming of Finite Element Solvers
Nonlinear Problems
Solid Mechanics Applications
Fluid Mechanics Applications
Coupled Problems
Appendices
Mathematical Topics
Diffpack Topics
Iterative Methods for Sparse Linear Systems
Software Tools for Solving Linear Systems