A B-spline finite element method for nonlinear differential equations describing crystal surface growth with variable coefficient

Abstract In this paper, an efficient finite element scheme is presented for a class of fourth-order nonlinear parabolic problems with variable coefficient. To deal with second-order term in weak formulation, we choose the cubic B-spline function as a trial function. Rigorous error estimates are deri...

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Main Authors:	Dandan Qin, Yanwei Du, Bo Liu, Wenzhu Huang
Format:	Article
Language:	English
Published:	SpringerOpen 2019-05-01
Series:	Advances in Difference Equations
Subjects:	Cubic B-spline Finite element method Nonlinear parabolic equation Variable coefficient Error estimate
Online Access:	http://link.springer.com/article/10.1186/s13662-019-2032-5

id	doaj-6ba58e6acacf4bdf91df9273f4faa27b
record_format	Article
spelling	doaj-6ba58e6acacf4bdf91df9273f4faa27b2020-11-25T02:00:30ZengSpringerOpenAdvances in Difference Equations1687-18472019-05-012019111610.1186/s13662-019-2032-5A B-spline finite element method for nonlinear differential equations describing crystal surface growth with variable coefficientDandan Qin0Yanwei Du1Bo Liu2Wenzhu Huang3College of Mathematics, Jilin UniversityCollege of Mathematics, Jilin UniversityCollege of Mathematics, Jilin UniversitySchool of Biology and Engineering, Guizhou Medical UniversityAbstract In this paper, an efficient finite element scheme is presented for a class of fourth-order nonlinear parabolic problems with variable coefficient. To deal with second-order term in weak formulation, we choose the cubic B-spline function as a trial function. Rigorous error estimates are derived for both semi-discrete and fully-discrete schemes. We provide a numerical example to confirm our theoretical results.http://link.springer.com/article/10.1186/s13662-019-2032-5Cubic B-splineFinite element methodNonlinear parabolic equationVariable coefficientError estimate
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Dandan Qin Yanwei Du Bo Liu Wenzhu Huang
spellingShingle	Dandan Qin Yanwei Du Bo Liu Wenzhu Huang A B-spline finite element method for nonlinear differential equations describing crystal surface growth with variable coefficient Advances in Difference Equations Cubic B-spline Finite element method Nonlinear parabolic equation Variable coefficient Error estimate
author_facet	Dandan Qin Yanwei Du Bo Liu Wenzhu Huang
author_sort	Dandan Qin
title	A B-spline finite element method for nonlinear differential equations describing crystal surface growth with variable coefficient
title_short	A B-spline finite element method for nonlinear differential equations describing crystal surface growth with variable coefficient
title_full	A B-spline finite element method for nonlinear differential equations describing crystal surface growth with variable coefficient
title_fullStr	A B-spline finite element method for nonlinear differential equations describing crystal surface growth with variable coefficient
title_full_unstemmed	A B-spline finite element method for nonlinear differential equations describing crystal surface growth with variable coefficient
title_sort	b-spline finite element method for nonlinear differential equations describing crystal surface growth with variable coefficient
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2019-05-01
description	Abstract In this paper, an efficient finite element scheme is presented for a class of fourth-order nonlinear parabolic problems with variable coefficient. To deal with second-order term in weak formulation, we choose the cubic B-spline function as a trial function. Rigorous error estimates are derived for both semi-discrete and fully-discrete schemes. We provide a numerical example to confirm our theoretical results.
topic	Cubic B-spline Finite element method Nonlinear parabolic equation Variable coefficient Error estimate
url	http://link.springer.com/article/10.1186/s13662-019-2032-5
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A B-spline finite element method for nonlinear differential equations describing crystal surface growth with variable coefficient

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