Lecture Notes

Lecture notes, Mats G. Larson

The lecture notes are divided into multiple files:

  1. Crash course
  2. Lectures 1 to 3 (or 4):
  3. 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:

    1. Overview of lectures and open problems
    2. Practical aspects of the dual weighted residual (DWR) method
    3. Nonstandard linear problems
    4. Nonlinear problems
    5. Application in solid mechanics
    6. Application in fluid mechanics
    7. Model adaptivity
    8. Application in optimal control
    9. Application in parameter estimation

    Suggested Reading

    1. 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
    2. 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.
    3. 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.
    4. A review of a posteriori error estimation and adaptive mesh-refinement techniques, Rüdiger Verfürth, Wiley-Teubner
    5. A Posterori Error Estimation in Finite Element Analysis, Mark Ainsworth and J. Tinsley Oden, Wiley-Interscience; 1st edition (January 15, 2000)
    6. 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).
    7. 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.
    8. 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.

    Published October 20, 2010