A two level algorithm for an obstacle problem

Fei Wang, Joseph Eichholz and Weimin Han

Applied Mathematics and Computation, 2018, vol. 330, issue C, 65-76

Abstract: Due to the inequality feature of the obstacle problem, the standard quadratic finite element method for solving the problem can only achieve an error bound of the form O(N−3/4+ϵ),N being the total number of degrees of freedom, and ϵ > 0 arbitrary. To achieve a better error bound, the key lies in how to capture the free boundary accurately. In this paper, we propose a two level algorithm for solving the obstacle problem. The first part of the algorithm is through the use of the linear elements on a quasi-uniform mesh. Then information on the approximate free boundary from the linear element solution is used in the construction of a quadratic finite element method. Under some assumptions, it is shown that the numerical solution from the two level algorithm is expected to have a nearly optimal error bound of O(N−1+ϵ), ϵ > 0 arbitrary. Such an expected convergence order is observed numerically in numerical examples.

Keywords: Variational inequality; Free-boundary problem; Quadratic elements; Error estimation; Optimal convergence order (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300318301322
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:330:y:2018:i:c:p:65-76

DOI: 10.1016/j.amc.2018.02.030

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().