A posteriori error estimates for fully discrete fractional-step $\vartheta$-approximations for the heat equation

Karakatsani Fotini

A posteriori error estimates for fully discrete fractional-step $\vartheta$-approximations for the heat equation

Numerical Analysis 2014-04-03 v1

Authors: Karakatsani Fotini

Abstract

We derive optimal order a posteriori error estimates for fully discrete approximations of the initial-boundary value problem for the heat equation. For the discretization in time we apply the fractional-step $\vartheta$ -scheme and for the discretization in space the finite element method with finite element spaces that are allowed to change with time. The first optimal order a posteriori error estimates in $L^\infty(0, T ; L^2({\varOmega}))$ are derived by applying the reconstruction technique.

Keywords

heat equation a posteriori error estimates fractional-step $\vartheta$-scheme finite element method reconstruction technique fully discrete approximations

Cite

@article{arxiv.1404.0497,
  title  = {A posteriori error estimates for fully discrete fractional-step $\vartheta$-approximations for the heat equation},
  author = {Karakatsani Fotini},
  journal= {arXiv preprint arXiv:1404.0497},
  year   = {2014}
}

Comments

22 pages, 6 figures

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