University of Sussex
Browse

File(s) not publicly available

Optimal order a posteriori error estimates for a class of Runge-Kutta and Galerkin methods

journal contribution
posted on 2023-06-08, 14:59 authored by George Akrivis, Charalambos MakridakisCharalambos Makridakis, Ricardo H Nochetto
We derive a posteriori error estimates, which exhibit optimal global order, for a class of time stepping methods of any order that include Runge–Kutta Collocation (RK-C) methods and the continuous Galerkin (cG) method for linear and nonlinear stiff ODEs and parabolic PDEs. The key ingredients in deriving these bounds are appropriate one-degree higher continuous reconstructions of the approximate solutions and pointwise error representations. The reconstructions are based on rather general orthogonality properties and lead to upper and lower bounds for the error regardless of the time-step; they do not hinge on asymptotics.

History

Publication status

  • Published

Journal

Numerische Mathematik

ISSN

0029-599X

Publisher

Springer Verlag

Issue

1

Volume

114

Page range

133-160

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2013-05-21

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC