Title:

Twosided a posteriori estimates of global and local errors for linear elliptic type boundary value problems (English) 
Author:

Hannukainen, Antti 
Author:

Korotov, Sergey 
Language:

English 
Journal:

Programs and Algorithms of Numerical Mathematics 
Volume:

Proceedings of Seminar. Prague, May 2831, 2006 
Issue:

2006 
Year:


Pages:

92103 
. 
Category:

math 
. 
Summary:

The paper is devoted to the problem of reliable control of accuracy of approximate solutions obtained in computer simulations. This task is strongly related to the socalled a posteriori error estimates, giving computable bounds for computational
errors and detecting zones in the solution domain, where such errors are too large and certain mesh refinements should be performed. Mathematical model described by a linear elliptic (reactiondiffusion) equation with mixed boundary conditions is considered. We derive in a simple way twosided (upper and lower) easily computable estimates for global (in terms of the energy norm) and local (in terms of linear functionals with local supports) control of the computational error, which is understood as the difference between the exact solution of the model and the approximation. Such twosided estimates are completely independent of the numerical technique used to obtain approximations and can be made as close to the true errors as resources of a concrete computer used for computations allow. (English) 
Keyword:

a posteriori error estimation 
Keyword:

error control in energy norm 
Keyword:

error control in terms of linear functionals 
Keyword:

reactiondiffusion equation 
Keyword:

mixed boundary conditions 
. 
Date available:

20150908T11:25:04Z 
Last updated:

20230605 
Stable URL:

http://hdl.handle.net/10338.dmlcz/702824 
. 