Helsinki University of Technology
Institute of Mathematics

Mat-5.210 Special Course in Computational Mechanics
Autumn 2006: "A Posteriori analysis for PDE's" (2 ocr)

S. Repin, V.A. Steklov Institute of Mathematics in St.-Petersburg


In the lecture course, an overview of a posteriori methods used in modern numerical analysis is exposed. The main purpose is to present (at least for certain classes of partial differential equations) a mathematically justified and practically efficient answer to the question:

How to verify the accuracy of approximate solutions computed by various numerical methods?

In the course, main ideas that form the basis of various a posteriori error estimation methods are discussed. A considerable part of the course is devoted to a new functional approach to a posteriori error control of PDE's developed in the recent decade. A special attention is paid on a posteriori estimates for mixed finite element approximations and approximations of problems in the theory of viscous fluids.


The lectures are given by Visiting Professor Sergey Repin on Wednesdays at 12-14 in the room U322 and on Fridays at 8-10 in the room U356. The first lecture is on Wednesday 4.10.2006. There are no lectures during the exam period 26.10.-1.11.


The course is oriented towards students and young scientists. The basic knowledge of differential calculus, functional analysis and finite element methods form a sufficient background to follow the course.

Course Material

The course material is announced during the lectures and on the course homepage.

  • Lecture Plan (PDF)
  • Lecture Notes (PDF)
  • Additional Information

    The course values 2 old credits (ov) and the requirements for passing the course consist of homework assignments. Listeners interested in a deeper investigation of the subject will be supplied with the literature and special research type tasks.

    The course assistant is Antti Niemi.

    Last Update: 6.9.2006