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Article

Segeth, Karel ; Šolín, Pavel
On some a posteriori error estimation results for the method of lines. (English). In: Chleboun, J., Segeth, K. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Prague, May 28-31, 2006. Institute of Mathematics AS CR, Prague, 2006. pp. 229-234
Summary:
The paper is an attempt to present an (incomplete) historical survey of some basic results of residual type estimation procedures from the beginning of their development through contemporary results to future prospects. Recently we witness a rapidly increasing use of the $hp$-FEM which is due to the well-established theory. However, the conventional a posteriori error estimates (in the form of a single number per element) are not enough here, more complex estimates are needed, and this can be the way to obtain them.
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