Winter School 2004: Lecture Notes and Suggested Reading
Lecture notes, Mats G. Larson
The lecture notes are divided into multiple files:
- Crash course
- Lectures 1 to 3 (or 4):
- Lectures 4-5, applications
Lecture notes, Rolf Rannacher
The lecture notes contain almost all the transparencies that will be presented. The material comprises a coverpage, 8 chapters and a two-page Outlook, a total of 120 pages. Since it includes many figures, the notes have been cut into several PDF files:
- Overview of lectures and open problems
- Practical aspects of the dual weighted residual (DWR) method
- Nonstandard linear problems
- Nonlinear problems
- Application in solid mechanics
- Application in fluid mechanics
- Model adaptivity
- Application in optimal control
- Application in parameter estimation
Suggested Reading
- Computational differential equations, Eriksson, K.; Estep, D.; Hansbo, P.; Johnson, C.. Cambridge University Press, Cambridge, 1996. xvi+538 pp. ISBN: 0-521-56312-7; 0-521-56738-6
- Introduction to adaptive methods for differential equations, Eriksson, Kenneth;Estep, Don; Hansbo, Peter; Johnson, Claes, Acta numerica, 1995,105--158, Acta Numer., Cambridge Univ. Press, Cambridge, 1995.
- Estimating the error of numerical solutions of systems of reaction-diffusion equations, Estep, Donald J, Larson, Mats G, and Williams, Roy D.. Mem. Amer. Math. Soc. 146(2000), no. 696, viii+109 pp.
- A review of a posteriori error estimation and adaptive mesh-refinement techniques, Rüdiger Verfürth, Wiley-Teubner
- A Posterori Error Estimation in Finite Element Analysis, Mark Ainsworth and J. Tinsley Oden, Wiley-Interscience; 1st edition (January 15, 2000)
- Adaptive Finite Element Methods for Differential Equations, W. Bangerth and R. Rannacher, Lectures in Mathematics, ETH Zürich, Birkhäuser, Basel 2003, (210 pages, Material presented in a course at the ERT Zürich, Summer 2002).
- An optimal control approach to error estimation and mesh adaptation in finite element methods, R. Becker and R. Rannacher, Acta Numerica 2000 (A. Iserles, ed.), pp. 1-102, Cambridge University Press, 2001.
- Adaptive finite element methods for low-Mach-number flows with chemical reactions, M. Braack and R. Rannacher (93 pages), in 30th Computational Fluid Dynamics (H. Deconinck, ed.), Volume 1999-03, Lecture Series, von Karman Institute of Fluid Dynamics, Brussels, 1999.