University of Sussex
Browse

File(s) not publicly available

A priori and a posteriori analysis of non-conforming finite elements with face penalty for advection-diffusion equations

journal contribution
posted on 2023-06-07, 19:14 authored by L El Alaoui, A Ern, E Burman
We analyse a non-conforming finite-element method to approximate advectiondiffusionreaction equations. The method is stabilized by penalizing the jumps of the solution and those of its advective derivative across mesh interfaces. The a priori error analysis leads to (quasi-)optimal estimates in the mesh size (sub-optimal by order in the L2-norm and optimal in the broken graph norm for quasi-uniform meshes) keeping the Pclet number fixed. Then, we investigate a residual a posteriori error estimator for the method. The estimator is semi-robust in the sense that it yields lower and upper bounds of the error which differ by a factor equal at most to the square root of the Pclet number. Finally, to illustrate the theory we present numerical results including adaptively generated meshes.

History

Publication status

  • Published

Journal

IMA Journal of Numerical Analysis

ISSN

0272-4979

Publisher

Oxford University Press

Issue

1

Volume

27

Page range

151-171

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