A review of some a posteriori error estimates for adaptive

Prof. Karel Segeth

May 19, 2009, 2:30 p.m. HS 14

Recently, the adaptive nite element methods have gained a very important position among numerical procedures for solving ordinary as well as partial di erential equations arising from various technical applications. While the classical a posteriori error estimates are oriented to the use in h-methods the contemporary higher-order hp-methods usually require new approaches in a posteriori error estimation as the task in every step of the hp-adaptive method is to nd a proper combination of spatial re nement with simultaneous variation of the polynomial order of the approximation.

We present a review of error estimation procedures for some particular both linear and nonlinear di erential problems with special regards to the needs of the hp-method.