Mat-1.3656 Numeerisen analyysin ja laskennallisen tieteen seminaari.

Ma 23.4. 2007

Professor Michal Krizek
Institute of Mathematics
Czech Academy of Sciences

Finite element approximation of a nonlinear heat conduction problem in anisotropic media

We give a survey of results which were obtained in solving a
stationary nonlinear heat conduction problem by the finite element method.
In particular, we present uniqueness theorems for the classical and weak
solutions, a comparison theorem, existence theorems for the weak and
finite element solutions, approximation of a curved boundary and numerical
inetgration, a discrete maximum principle, convergence without any
regularity assumptions, a priori error estimates, nonlinear boundary
conditions and numerical algorithms.