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Method for constructing meshes adapting to the solution of boundary value problems for ordinary differential equations of the second and fourth ordersстатья
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: 2 октября 2014 г.
- Авторы: Zolotareva N.D., Nikolaev E.S.
- Журнал: Differential Equations
- Том: 45
- Номер: 8
- Год издания: 2009
- Издательство: Pleiades Publishing, Inc.
- Местоположение издательства: New York, USA
- Первая страница: 1189
- Последняя страница: 1202
- DOI: 10.1134/S0012266109080102
- Аннотация: To solve boundary value problems for ordinary differential equations of the second and fourth orders, we suggest a method for constructing a sequence of adaptively refined and coarsened meshes in a version of the finite element method with piecewise cubic Hermite basis functions. The construction of the meshes is based on C-norm estimates of the variation in the approximate solution or in the value of the functional to be minimized under the addition of a test point to a mesh interval or the deletion of a point from the current mesh. We present the results of numerical experiments used to assess the efficiency of the method. By way of example, problems whose solutions have singularities of the boundary layer type were used in these experiments. We carry out a comparison with a version of the method based on the uniform mesh refinement.
- Добавил в систему: Николаев Евгений Сергеевич