High Accuracy Analysis of Nonconforming Mixed Finite Element Method for the Nonlinear Sivashinsky Equation

High Accuracy Analysis of Nonconforming Mixed Finite Element Method for the Nonlinear Sivashinsky Equation

The fourth-order nonlinear Sivashinsky equation is often used to simulate a planar solid-liquid interface for a binary alloy. In this paper, we study the high accuracy analysis of the nonconforming mixed finite element method (MFEM for short) for this equation. Firstly, by use of the special propert...

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Main Authors: Lele Wang, Xin Liao
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2020/8416898
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spelling doaj-59bcd8f989264d88bfe31abe84488bda2020-11-25T02:04:34ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472020-01-01202010.1155/2020/84168988416898High Accuracy Analysis of Nonconforming Mixed Finite Element Method for the Nonlinear Sivashinsky EquationLele Wang0Xin Liao1School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou 450046, ChinaSchool of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou 450046, ChinaThe fourth-order nonlinear Sivashinsky equation is often used to simulate a planar solid-liquid interface for a binary alloy. In this paper, we study the high accuracy analysis of the nonconforming mixed finite element method (MFEM for short) for this equation. Firstly, by use of the special property of the nonconforming EQ1rot element (see Lemma 1), the superclose estimates of order Oh2+Δt in the broken H1-norm for the original variable u and intermediate variable p are deduced for the back-Euler (B-E for short) fully-discrete scheme. Secondly, the global superconvergence results of order Oh2+Δt for the two variables are derived through interpolation postprocessing technique. Finally, a numerical example is provided to illustrate validity and efficiency of our theoretical analysis and method.http://dx.doi.org/10.1155/2020/8416898
collection DOAJ
language English
format Article
sources DOAJ
author Lele Wang
Xin Liao
spellingShingle Lele Wang
Xin Liao
High Accuracy Analysis of Nonconforming Mixed Finite Element Method for the Nonlinear Sivashinsky Equation
Mathematical Problems in Engineering
author_facet Lele Wang
Xin Liao
author_sort Lele Wang
title High Accuracy Analysis of Nonconforming Mixed Finite Element Method for the Nonlinear Sivashinsky Equation
title_short High Accuracy Analysis of Nonconforming Mixed Finite Element Method for the Nonlinear Sivashinsky Equation
title_full High Accuracy Analysis of Nonconforming Mixed Finite Element Method for the Nonlinear Sivashinsky Equation
title_fullStr High Accuracy Analysis of Nonconforming Mixed Finite Element Method for the Nonlinear Sivashinsky Equation
title_full_unstemmed High Accuracy Analysis of Nonconforming Mixed Finite Element Method for the Nonlinear Sivashinsky Equation
title_sort high accuracy analysis of nonconforming mixed finite element method for the nonlinear sivashinsky equation
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2020-01-01
description The fourth-order nonlinear Sivashinsky equation is often used to simulate a planar solid-liquid interface for a binary alloy. In this paper, we study the high accuracy analysis of the nonconforming mixed finite element method (MFEM for short) for this equation. Firstly, by use of the special property of the nonconforming EQ1rot element (see Lemma 1), the superclose estimates of order Oh2+Δt in the broken H1-norm for the original variable u and intermediate variable p are deduced for the back-Euler (B-E for short) fully-discrete scheme. Secondly, the global superconvergence results of order Oh2+Δt for the two variables are derived through interpolation postprocessing technique. Finally, a numerical example is provided to illustrate validity and efficiency of our theoretical analysis and method.
url http://dx.doi.org/10.1155/2020/8416898
work_keys_str_mv AT lelewang highaccuracyanalysisofnonconformingmixedfiniteelementmethodforthenonlinearsivashinskyequation
AT xinliao highaccuracyanalysisofnonconformingmixedfiniteelementmethodforthenonlinearsivashinskyequation
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