Functional A Posteriori Error Estimates for the Parabolic Obstacle Problem-Reference-Cited by-同舟云学术

Functional A Posteriori Error Estimates for the Parabolic Obstacle Problem

Published:2022-01-23 Issue:2 Volume:22 Page:259-276
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Apushkinskaya Darya¹,Repin Sergey²

Affiliation:

1. Saarland University , 66041 Saarbrücken , Germany ; and Peoples’ Friendship University of Russia (RUDN University), 117198 Moscow, Russia

2. V. A. Steklov Institute of Mathematics in St. Petersburg, 191011 St. Petersburg , Russia ; and University of Jyväskylä, 40014 Jyväskylä, Finland

Abstract

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.

Funder

Deutsche Forschungsgemeinschaft

Russian Foundation for Basic Research

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/cmam-2021-0156/pdf

Reference55 articles.

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