Finite element methods for semilinear elliptic problems with smooth interfaces

Bhupen Deka () and Tazuddin Ahmed ()
Additional contact information
Bhupen Deka: Tezpur University
Tazuddin Ahmed: Tezpur University

Indian Journal of Pure and Applied Mathematics, 2011, vol. 42, issue 4, 205-223

Abstract: Abstract The purpose of this paper is to study the finite element method for second order semilinear elliptic interface problems in two dimensional convex polygonal domains. Due to low global regularity of the solution, it seems difficult to achieve optimal order of convergence with straight interface triangles [Numer. Math., 79 (1998), pp. 175–202]. For a finite element discretization based on a mesh which involve the approximation of the interface, optimal order error estimates in L 2 and H 1-norms are proved for linear elliptic interface problem under practical regularity assumptions of the true solution. Then an extension to the semilinear problem is also considered and optimal error estimate in H 1 norm is achieved.

Keywords: Elliptic; interface; semilinear; finite element method; optimal error estimate (search for similar items in EconPapers)
Date: 2011
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s13226-011-0014-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:indpam:v:42:y:2011:i:4:d:10.1007_s13226-011-0014-8

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-011-0014-8

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().