A1 Journal article (refereed)
Functional A Posteriori Error Estimates for the Parabolic Obstacle Problem (2022)


Apushkinskaya, D., & Repin, S. (2022). Functional A Posteriori Error Estimates for the Parabolic Obstacle Problem. Computational Methods in Applied Mathematics, 22(2), 259-276. https://doi.org/10.1515/cmam-2021-0156


JYU authors or editors


Publication details

All authors or editors: Apushkinskaya, Darya; Repin, Sergey

Journal or series: Computational Methods in Applied Mathematics

ISSN: 1609-4840

eISSN: 1609-9389

Publication year: 2022

Publication date: 23/01/2022

Volume: 22

Issue number: 2

Pages range: 259-276

Publisher: Walter de Gruyter GmbH

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1515/cmam-2021-0156

Publication open access: Not open

Publication channel open access:

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2109.14519


Abstract

The paper is concerned with functional-type a posteriori estimates for the initial boundary value problem for a parabolic partial differential equation with an obstacle. We deduce a guaranteed and computable bound of the distance between the exact minimizer and any function from the admissible (energy) class of functions. Applications to the analysis of modeling errors caused by data implification are discussed. An important case of time incremental approximations is specially studied. Numerical examples presented in the last section show how the estimates work in practice.


Keywords: partial differential equations; numerical analysis; estimating (statistical methods); error analysis

Free keywords: parabolic obstacle problem; free boundary; functional a posteriori error estimates


Contributing organizations


Ministry reporting: Yes

Reporting Year: 2022

Preliminary JUFO rating: 1


Last updated on 2022-19-08 at 20:17