---
_id: '55078'
abstract:
- lang: eng
  text: "This paper develops and discusses a residual-based a posteriori error\r\nestimate
    and a space--time adaptive algorithm for solving parabolic surface\r\npartial
    differential equations on closed stationary surfaces. The full\r\ndiscretization
    uses the surface finite element method in space and the backward\r\nEuler method
    in time. The proposed error indicator bounds the error quantities\r\nglobally
    in space from above and below, and globally in time from above and\r\nlocally
    from below. A space--time adaptive algorithm is proposed using the\r\nderived
    error indicator. Numerical experiments illustrate and complement the\r\ntheory."
author:
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Michael Frederik Raúl
  full_name: Lantelme, Michael Frederik Raúl
  id: '102867'
  last_name: Lantelme
citation:
  ama: Kovács B, Lantelme MFR. A posteriori error estimates for parabolic partial
    differential equations on stationary surfaces. <i>arXiv:240702101</i>. Published
    online 2024.
  apa: Kovács, B., &#38; Lantelme, M. F. R. (2024). A posteriori error estimates for
    parabolic partial differential equations on stationary surfaces. In <i>arXiv:2407.02101</i>.
  bibtex: '@article{Kovács_Lantelme_2024, title={A posteriori error estimates for
    parabolic partial differential equations on stationary surfaces}, journal={arXiv:2407.02101},
    author={Kovács, Balázs and Lantelme, Michael Frederik Raúl}, year={2024} }'
  chicago: Kovács, Balázs, and Michael Frederik Raúl Lantelme. “A Posteriori Error
    Estimates for Parabolic Partial Differential Equations on Stationary Surfaces.”
    <i>ArXiv:2407.02101</i>, 2024.
  ieee: B. Kovács and M. F. R. Lantelme, “A posteriori error estimates for parabolic
    partial differential equations on stationary surfaces,” <i>arXiv:2407.02101</i>.
    2024.
  mla: Kovács, Balázs, and Michael Frederik Raúl Lantelme. “A Posteriori Error Estimates
    for Parabolic Partial Differential Equations on Stationary Surfaces.” <i>ArXiv:2407.02101</i>,
    2024.
  short: B. Kovács, M.F.R. Lantelme, ArXiv:2407.02101 (2024).
date_created: 2024-07-04T12:53:47Z
date_updated: 2026-02-18T14:45:36Z
department:
- _id: '841'
external_id:
  arxiv:
  - '2407.02101'
language:
- iso: eng
publication: arXiv:2407.02101
status: public
title: A posteriori error estimates for parabolic partial differential equations on
  stationary surfaces
type: preprint
user_id: '100441'
year: '2024'
...