A nodally bound-preserving finite element method for time-dependent convection–diffusion equations

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Amiri, Abdolreza and Barrenechea, Gabriel R. and Pryer, Tristan (2025) A nodally bound-preserving finite element method for time-dependent convection–diffusion equations. Journal of Computational and Applied Mathematics, 470. 116691. ISSN 0377-0427 (https://doi.org/10.1016/j.cam.2025.116691)

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Abstract

This paper presents a new method to approximate the time-dependent convection–diffusion equations using conforming finite element methods, ensuring that the discrete solution respects the physical bounds imposed by the differential equation. The method is built by defining, at each time step, a convex set of admissible finite element functions (that is, the ones that satisfy the global bounds at their degrees of freedom) and seeks for a discrete solution in this admissible set. A family of θ-schemes is used as time integrators, and well-posedness of the discrete schemes is proven for the whole family, but stability and optimal-order error estimates are proven for the implicit Euler scheme. Nevertheless, our numerical experiments show that the method also provides stable and optimally-convergent solutions when the Crank–Nicolson method is used.

ORCID iDs

Amiri, Abdolreza, Barrenechea, Gabriel R. ORCID logoORCID: https://orcid.org/0000-0003-4490-678X and Pryer, Tristan;
  • Item type:Article
    ID code:92680
    Dates:
    Date
    Event
    15 December 2025
    Published
    17 April 2025
    Published Online
    4 April 2025
    Accepted
    16 May 2023
    Submitted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:25 Apr 2025 07:43
    Last modified:09 May 2025 07:56
    URI:https://strathprints.strath.ac.uk/id/eprint/92680
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