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<p>In the present paper, we establish the well-posedness, stability, and (weak) convergence of a fully-discrete approximation of the unsteady <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="211_2025_1450_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(p(\cdot ,\cdot )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mo>·</mo> <mo>,</mo> <mo>·</mo> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-Navier–Stokes equations employing an implicit Euler step in time and a discretely inf-sup-stable finite element approximation&#xa0;in&#xa0;space.&#xa0;Moreover, numerical experiments are carried out that supplement the theoretical findings.</p>

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Convergence analysis for a fully-discrete finite element approximation of the unsteady \(p(\cdot ,\cdot )\)-Navier–Stokes equations

  • 期刊论文

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  • 发表日期：

    2025年2月25日

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  • Luigi C. Berselli,
  • Alex Kaltenbach

摘要

In the present paper, we establish the well-posedness, stability, and (weak) convergence of a fully-discrete approximation of the unsteady \(p(\cdot ,\cdot )\) p ( · , · ) -Navier–Stokes equations employing an implicit Euler step in time and a discretely inf-sup-stable finite element approximation in space. Moreover, numerical experiments are carried out that supplement the theoretical findings.