Blending low-order stabilised finite element methods : a positivity-preserving local projection method for the convection-diffusion equation

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Barrenechea, Gabriel and Burman, Erik and Karakatsani, Fotini (2017) Blending low-order stabilised finite element methods : a positivity-preserving local projection method for the convection-diffusion equation. Computer Methods in Applied Mechanics and Engineering, 317. pp. 1169-1193. ISSN 0045-7825 (https://doi.org/10.1016/j.cma.2017.01.016)

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Abstract

In this work we propose a nonlinear blending of two low-order stabilisation mechanisms for the convection-diffusion equation. The motivation for this approach is to preserve monotonicity without sacrificing accuracy for smooth solutions. The approach is to blend a first-order artificial diffusion method, which will be active only in the vicinity of layers and extrema, with an optimal order local projection stabilisation method that will be active on the smooth regions of the solution. We prove existence of discrete solutions, as well as convergence, under appropriate assumptions on the nonlinear terms, and on the exact solution. Numerical examples show that the discrete solution produced by this method remains within the bounds given by the continuous maximum principle, while the layers are not smeared significantly.

ORCID iDs

Barrenechea, Gabriel ORCID logoORCID: https://orcid.org/0000-0003-4490-678X, Burman, Erik and Karakatsani, Fotini;
  • Item type:Article
    ID code:60250
    Dates:
    Date
    Event
    15 April 2017
    Published
    20 January 2017
    Published Online
    10 January 2017
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:20 Mar 2017 14:15
    Last modified:18 Dec 2024 01:20
    URI:https://strathprints.strath.ac.uk/id/eprint/60250
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