Asymptotic Domain Decomposition and a Posteriori Estimates for a Semi Linear Problem

Pousin, Jerome and Slimani, Kamel (2012) Asymptotic Domain Decomposition and a Posteriori Estimates for a Semi Linear Problem. British Journal of Mathematics & Computer Science, 2 (4). pp. 226-241. ISSN 22310851

[thumbnail of Pousin-242012BJMCS1632.pdf] Text
Pousin-242012BJMCS1632.pdf - Published Version

Download (735kB)


Coupling heterogeneous mathematical models is today commonly used, and effective solution methods for the resulting hybrid problem have recently become available for several systems. Even if in certain circumstances, asymptotic evaluations of the location of the interfaces are available, no strategy are proposed for locating the interfaces in numerical simulations. In this article, a semilinear elliptic problem is considered. By reformulating the problem in a mixed formulation context and by using an a posteriori error estimate, we propose an indicator of the error due to a wrong position of the junction. Minimizing this indicator allows us to determine accurately the location of the junction. By comparing this indicator with a mesh error indicator, this allows to decide if it is better to refine the mesh or to move the interface. Some numerical results are presented showing the efficiency of the proposed indicator.

Item Type: Article
Subjects: Eprints STM archive > Mathematical Science
Depositing User: Unnamed user with email admin@eprints.stmarchive
Date Deposited: 23 Jun 2023 05:07
Last Modified: 04 Dec 2023 03:59

Actions (login required)

View Item
View Item