Discrete Dynamics in Nature and Society
Volume 4 (2000), Issue 4, Pages 269-281

The dirichlet boundary conditions and related natural boundary conditions in strengthened sobolev spaces for discretized parabolic problems

E. D'Yakonov

Department of Computer Mathematics and Cybernetics, Moscow State University, Moscow 119899, Russia

Received 21 April 1999

Copyright © 2000 E. D'Yakonov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Correctness of initial boundary value problems and their discretizations are analyzed under unusual second-order boundary conditions, which can be considered as natural boundary conditions in strengthened Sobolev spaces and as improvements (in some cases) of the classical Dirichlet boundary conditions. Special attention is paid to optimal perturbation estimates for new variants of the penalty method with respect to the Dirichlet conditions.