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<p>In this article, a space-time finite element method (STFEM) for time fractional-order reaction-diffusion equations (TFORDEs) containing fractional derivatives of order <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2366_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="69" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \in (0,1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> with initial data and boundary value. Utilizing the variational formulation, we establish a space-time finite element framework for addressing the problem. Additionally, we derive a posterior error estimators for both spatial and temporal components, and based on these estimators, we develop an adaptive algorithm. The effectiveness of this adaptive algorithm is ultimately demonstrated through a series of numerical experiments.</p>

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Adaptive space-time finite element method for time fractional-order reaction-diffusion equations

  • 期刊论文

  • 发表日期：

    2025年1月8日

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  • Man Li,
  • Liang Ge

摘要

In this article, a space-time finite element method (STFEM) for time fractional-order reaction-diffusion equations (TFORDEs) containing fractional derivatives of order \(\alpha \in (0,1)\) α ∈ ( 0 , 1 ) with initial data and boundary value. Utilizing the variational formulation, we establish a space-time finite element framework for addressing the problem. Additionally, we derive a posterior error estimators for both spatial and temporal components, and based on these estimators, we develop an adaptive algorithm. The effectiveness of this adaptive algorithm is ultimately demonstrated through a series of numerical experiments.