University of Sussex
Browse

File(s) not publicly available

Finite element methods with symmetric stabilization for the transient convection-diffusion-reaction equation

journal contribution
posted on 2023-06-08, 05:12 authored by Erik Burman, Miguel A Fernández
We consider implicit and semi-implicit time-stepping methods for finite element approximations of singularly perturbed parabolic problems or hyperbolic problems. We are interested in problems where the advection dominates and stability is obtained using a symmetric, weakly consistent stabilization operator in the finite element method. Several A-stable time discretizations are analyzed and shown to lead to unconditionally stable and optimally convergent schemes. In particular, we show that the contribution from the stabilization leading to an extended matrix pattern may be extrapolated from previous time steps, and hence handled explicitly without loss of stability and accuracy. A fully explicit treatment of the stabilization term is obtained under a CFL condition

History

Publication status

  • Published

Journal

Computer Methods in Applied Mechanics and Engineering

ISSN

0045-7825

Publisher

Elsevier

Issue

33

Volume

198

Page range

2508-2519

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC