Scholarlink

Abstract <p>This paper presents a two-grid method for solving nonlinear time fractional diffusion equations (TFDEs). First, a fully discrete scheme is constructed by using <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12258_2025_276_Article_IEq5.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">\(P_{0}^{2}-P_{1}\)</EquationSource> <!--NumAnAp2502007Hua-m5--> </InlineEquation> mixed finite elements (MFEs) and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12258_2025_276_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(L1\)</EquationSource> <!--NumAnAp2502007Hua-m6--> </InlineEquation> formula for spatial and temporal discretization, respectively. Second, the stability and error of the fully discrete scheme are analyzed. Third, a two-grid algorithm (TGA) based on the fully discrete scheme is proposed and its stability and error analysis results are derived. Finally, some numerical examples are provided to support the theoretical results.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Two-Grid \(\boldsymbol{P_{0}^{2}-P_{1}}\) MFE Combined with \(\boldsymbol{L1}\) Scheme for Nonlinear Fractional Diffusion Equations

  • 期刊论文

  • 发表日期：

    2025年6月1日

查看全文
  • Y. Hua,
  • Y. Tang,
  • Z. Chen

摘要

Abstract

This paper presents a two-grid method for solving nonlinear time fractional diffusion equations (TFDEs). First, a fully discrete scheme is constructed by using \(P_{0}^{2}-P_{1}\) mixed finite elements (MFEs) and \(L1\) formula for spatial and temporal discretization, respectively. Second, the stability and error of the fully discrete scheme are analyzed. Third, a two-grid algorithm (TGA) based on the fully discrete scheme is proposed and its stability and error analysis results are derived. Finally, some numerical examples are provided to support the theoretical results.