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A comparative analysis of adaptive algorithms in the finite element method for solving the boundary value problem for a stationary reaction – di ff usion equationстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 14 ноября 2016 г.
- Авторы: Zolotareva N.D., Nikolaev E.S.
- Журнал: Moscow University Computational Mathematics and Cybernetics
- Том: 40
- Номер: 3
- Год издания: 2016
- Издательство: Allerton Press Inc.
- Местоположение издательства: United States
- Первая страница: 97
- Последняя страница: 109
- DOI: 10.3103/S0278641916030080
- Аннотация: A new adaptive algorithm is proposed for constructing grids in the hp-version of the finite element method with piecewise polynomial basis functions. This algorithm allows us to find a solution (with local singularities) to the boundary value problem for a one-dimensional reaction–diffusion equation and smooth the grid solution via the adaptive elimination and addition of grid nodes. This algorithm is compared to one proposed earlier that adaptively refines the grid and deletes nodes with the help of an estimate for the local effect of trial addition of new basis functions and the removal of old ones. Results are presented from numerical experiments aimed at assessing the performance of the proposed algorithm on a singularly perturbed model problem with a smooth solution.
- Добавил в систему: Николаев Евгений Сергеевич