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<p>A ultra-weak discontinuous Galerkin finite element method for a series of time-fractional Burgers equations in one dimension is proposed. The method is based on <i>L</i>1 difference formula in time and ultra-weak discontinuous Galerkin formula in space. By carefully selecting interface numerical fluxes, we prove that the scheme is stable and it has optimal convergence order in the standard <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2024_862_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> norm. Finally, two numerical examples are presented to verify our theoretical analysis.</p>

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The ultra-weak discontinuous Galerkin method for time-fractional Burgers equation

  • 期刊论文

  • 发表日期：

    2025年1月8日

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  • Xiaoxiao Chen,
  • Yanli Chen

摘要

A ultra-weak discontinuous Galerkin finite element method for a series of time-fractional Burgers equations in one dimension is proposed. The method is based on L1 difference formula in time and ultra-weak discontinuous Galerkin formula in space. By carefully selecting interface numerical fluxes, we prove that the scheme is stable and it has optimal convergence order in the standard \(L^2\) L 2 norm. Finally, two numerical examples are presented to verify our theoretical analysis.