Error Analysis of Fully Discrete Data Assimilation Algorithms for Reaction-Diffusion Equation
Year: 2025
Author: Wansheng Wang, Chengyu Jin, Yi Huang
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 3 : pp. 840–866
Abstract
In this paper we propose a continuous downscaling data assimilation algorithm for solving reaction-diffusion equations with a critical parameter. For the spatial discretization we consider the finite element methods. Two backward differentiation formulae (BDF), a backward Euler method and a two-step backward differentiation formula, are employed for the time discretization. Employing the dissipativity property of the underlying reaction-diffusion equation, under suitable conditions on the relaxation (nudging) parameter and the critical parameter, we obtain uniform-in-time error estimates for all the methods for the error between the fully discrete approximation and the reference solution corresponding to the measurements given on a coarse mesh by an interpolation operator. Numerical experiments verify and complement our theoretical results.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2023-0150
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 3 : pp. 840–866
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Data assimilation reaction-diffusion equation finite element method BDF methods fully discrete uniform-in-time error estimates Allen-Cahn equation.
Author Details
Wansheng Wang Email
Chengyu Jin Email
Yi Huang Email