Some Second-Order <i>σ</i> Schemes Combined with an <i>H</i><sup>1</sup>-Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion Equation

Some Second-Order <i>σ</i> Schemes Combined with an <i>H</i><sup>1</sup>-Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion Equation

In this article, some high-order time discrete schemes with an <inline-formula> <math display="inline"> <semantics> <msup> <mi>H</mi> <mn>1</mn> </msup> </semantics> </math> </inline-formula>-Galerkin mixed finite elem...

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Main Authors: Yaxin Hou, Cao Wen, Hong Li, Yang Liu, Zhichao Fang, Yining Yang
Format: Article
Language:English
Published: MDPI AG 2020-02-01
Series:Mathematics
Subjects:
second-order <i>σ</i> scheme
interpolation approximation
<i>h</i><sup>1</sup>-galerkin mixed finite element method
nonlinear distributed-order sub-diffusion equation
stability
error estimates
Online Access:https://www.mdpi.com/2227-7390/8/2/187
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spelling doaj-e35f88be1cc4490d81f3e9344f9564712020-11-25T02:03:23ZengMDPI AGMathematics2227-73902020-02-018218710.3390/math8020187math8020187Some Second-Order <i>σ</i> Schemes Combined with an <i>H</i><sup>1</sup>-Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion EquationYaxin Hou0Cao Wen1Hong Li2Yang Liu3Zhichao Fang4Yining Yang5School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaIn this article, some high-order time discrete schemes with an <inline-formula> <math display="inline"> <semantics> <msup> <mi>H</mi> <mn>1</mn> </msup> </semantics> </math> </inline-formula>-Galerkin mixed finite element (MFE) method are studied to numerically solve a nonlinear distributed-order sub-diffusion model. Among the considered techniques, the interpolation approximation combined with second-order <inline-formula> <math display="inline"> <semantics> <mi>&#963;</mi> </semantics> </math> </inline-formula> schemes in time is used to approximate the distributed order derivative. The stability and convergence of the scheme are discussed. Some numerical examples are provided to indicate the feasibility and efficiency of our schemes.https://www.mdpi.com/2227-7390/8/2/187second-order <i>σ</i> schemeinterpolation approximation<i>h</i><sup>1</sup>-galerkin mixed finite element methodnonlinear distributed-order sub-diffusion equationstabilityerror estimates
collection DOAJ
language English
format Article
sources DOAJ
author Yaxin Hou
Cao Wen
Hong Li
Yang Liu
Zhichao Fang
Yining Yang
spellingShingle Yaxin Hou
Cao Wen
Hong Li
Yang Liu
Zhichao Fang
Yining Yang
Some Second-Order <i>σ</i> Schemes Combined with an <i>H</i><sup>1</sup>-Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion Equation
Mathematics
second-order <i>σ</i> scheme
interpolation approximation
<i>h</i><sup>1</sup>-galerkin mixed finite element method
nonlinear distributed-order sub-diffusion equation
stability
error estimates
author_facet Yaxin Hou
Cao Wen
Hong Li
Yang Liu
Zhichao Fang
Yining Yang
author_sort Yaxin Hou
title Some Second-Order <i>σ</i> Schemes Combined with an <i>H</i><sup>1</sup>-Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion Equation
title_short Some Second-Order <i>σ</i> Schemes Combined with an <i>H</i><sup>1</sup>-Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion Equation
title_full Some Second-Order <i>σ</i> Schemes Combined with an <i>H</i><sup>1</sup>-Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion Equation
title_fullStr Some Second-Order <i>σ</i> Schemes Combined with an <i>H</i><sup>1</sup>-Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion Equation
title_full_unstemmed Some Second-Order <i>σ</i> Schemes Combined with an <i>H</i><sup>1</sup>-Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion Equation
title_sort some second-order <i>σ</i> schemes combined with an <i>h</i><sup>1</sup>-galerkin mfe method for a nonlinear distributed-order sub-diffusion equation
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2020-02-01
description In this article, some high-order time discrete schemes with an <inline-formula> <math display="inline"> <semantics> <msup> <mi>H</mi> <mn>1</mn> </msup> </semantics> </math> </inline-formula>-Galerkin mixed finite element (MFE) method are studied to numerically solve a nonlinear distributed-order sub-diffusion model. Among the considered techniques, the interpolation approximation combined with second-order <inline-formula> <math display="inline"> <semantics> <mi>&#963;</mi> </semantics> </math> </inline-formula> schemes in time is used to approximate the distributed order derivative. The stability and convergence of the scheme are discussed. Some numerical examples are provided to indicate the feasibility and efficiency of our schemes.
topic second-order <i>σ</i> scheme
interpolation approximation
<i>h</i><sup>1</sup>-galerkin mixed finite element method
nonlinear distributed-order sub-diffusion equation
stability
error estimates
url https://www.mdpi.com/2227-7390/8/2/187
work_keys_str_mv AT yaxinhou somesecondorderisischemescombinedwithanihisup1supgalerkinmfemethodforanonlineardistributedordersubdiffusionequation
AT caowen somesecondorderisischemescombinedwithanihisup1supgalerkinmfemethodforanonlineardistributedordersubdiffusionequation
AT hongli somesecondorderisischemescombinedwithanihisup1supgalerkinmfemethodforanonlineardistributedordersubdiffusionequation
AT yangliu somesecondorderisischemescombinedwithanihisup1supgalerkinmfemethodforanonlineardistributedordersubdiffusionequation
AT zhichaofang somesecondorderisischemescombinedwithanihisup1supgalerkinmfemethodforanonlineardistributedordersubdiffusionequation
AT yiningyang somesecondorderisischemescombinedwithanihisup1supgalerkinmfemethodforanonlineardistributedordersubdiffusionequation
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