A stabilised finite element method for a fictitious domain problem allowing small inclusions

Barrenechea, Gabriel R. and Gonzalez Aguayo, Cheherazada (2018) A stabilised finite element method for a fictitious domain problem allowing small inclusions. Numerical Methods for Partial Differential Equations, 34 (1). pp. 167-183. ISSN 0749-159X (https://doi.org/10.1002/num.22190)

[thumbnail of Barrenechea-Gonzalez-NMPDE-2017-A-stabilised-finite-element-method-for-a-fictitious]
Preview
 Text. Filename: Barrenechea_Gonzalez_NMPDE_2017_A_stabilised_finite_element_method_for_a_fictitious.pdf
Accepted Author Manuscript
Download (928kB)| Preview

Abstract

The purpose of this work is to approximate numerically an elliptic partial differential equation posed on domains with small perforations (or inclusions). The approach is based on the fictitious domain method, and since the method's interest lies in the case in which the geometrical features are not resolved by the mesh, we propose a stabilised finite element method. The stabilisation term is a simple, non-consistent penalisation, that can be linked to the Barbosa-Hughes approach. Stability and optimal convergence are proved, and numerical results confirm the theory.

ORCID iDs

Barrenechea, Gabriel R. ORCID logoORCID: https://orcid.org/0000-0003-4490-678X and Gonzalez Aguayo, Cheherazada ORCID logoORCID: https://orcid.org/0000-0001-9488-9805;
  • Item type:Article
    ID code:61127
    Dates:
    Date
    Event
    1 January 2018
    Published
    24 November 2017
    Published Online
    27 June 2017
    Accepted
    22 August 2016
    Submitted
    Notes:© 2017 Wiley Periodicals, Inc. Barrenechea GR, González C. A stabilized finite element method for a fictitious domain problem allowing small inclusions. Numer Methods Partial Differential Eq. 2018; 34: 167–183. https://doi.org/10.1002/num.22190
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:28 Jun 2017 09:19
    Last modified:11 Nov 2024 11:44
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/61127
CORE (COnnecting REpositories)