Remarks on numerical experiments of the Allen-Cahn equations with constraint via Yosida approximation
type: Item
instance of: scholarly article
title: Remarks on numerical experiments of the Allen-Cahn equations with constraint via Yosida approximation
zbMATH Open document ID: 1422.65184
DOI: 10.1155/2016/1492812
author: Tomoyuki Suzuki
author: Keisuke Takasao
author: Noriaki Yamazaki
published in: Advances in Numerical Analysis
publication date: 2018-05-23T00:00:00Z
review text: Summary: We consider a one-dimensional Allen-Cahn equation with constraint from the viewpoint of numerical analysis. The constraint is provided by the subdifferential of the indicator function on the closed interval, which is the multivalued function. Therefore, it is very difficult to perform a numerical experiment of our equation. In this paper we approximate the constraint by the Yosida approximation. Then, we study the approximating system of the original model numerically. In particular, we give the criteria for the standard forward Euler method to give the stable numerical experiments of the approximating equation. Moreover, we provide the numerical experiments of the approximating equation.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 6871537
Wikidata QID: Q59123139
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/1492812
OpenAlex ID: W2409832930
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DBLP publication ID: journals/ana/SuzukiTY16
description: scientific article; zbMATH DE number 6871537