Scientific publications of the Ivan Franko National University of Lviv

Visnyk of the Lviv University. Series Applied Mathematics and Computer Science

Additional information
Year 2018
Volume 26
Authors Drebotiy R., Shynkarenko H.
Name of the article Elementwise decomposition of a posteriori error estimator based on reference solution for hp-adaptive finite element method
Abstract We consider the construction of a posteriori error estimator (AEE), based on the reference solution for one-dimensional hp-adaptive finite element method (FEM). It is shown that the square of the global error estimator can be represented as a sum of squares of single element error indicators, which are calculated independently on the elements of the selected mesh. The obtained decomposition can be used to justify the iterative algorithms of hp-adaptive FEM schemes. The proposed estimator can be used to calculate the error decrease rates for different local mesh refinement of just single finite element without re-calculating the entire reference solution on the whole problem domain. In addition, by choosing the system of Lobatto functions as a finite element basis, we propose an efficient scheme for calculating the local indicators.
Language English
PDF format Drebotiy R., Shynkarenko H. 
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