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<p>This paper presents a linearized backward Euler (BE) finite element scheme for the three-dimensional (3D) transient Stokes equations with damping (DS). Unconditional optimal error estimates of all variables are derived. A novel approach is employed to establish the boundedness of the numerical solutions, and the key is to bound the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2643_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^\infty\)</EquationSource> </InlineEquation>-norm by the Stokes operator. Ultimately, a numerical example is performed to validate the theoretical findings.</p>

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A novel convergence analysis of a linearized finite element scheme for the three-dimensional transient Stokes equations with damping

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Kesen Zhao,
  • Minghao Li,
  • Liuchao Xiao

摘要

This paper presents a linearized backward Euler (BE) finite element scheme for the three-dimensional (3D) transient Stokes equations with damping (DS). Unconditional optimal error estimates of all variables are derived. A novel approach is employed to establish the boundedness of the numerical solutions, and the key is to bound the \(L^\infty\) -norm by the Stokes operator. Ultimately, a numerical example is performed to validate the theoretical findings.