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<p>In this article, we consider parabolic interior layer singularly perturbed problems and we analyze the problem based on an implicit upwind algorithm on G-mesh in the spatial direction and uniform mesh in the temporal direction. We prove that the error estimate of the algorithm is <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2024_876_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(\epsilon\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϵ</mi> </math></EquationSource> </InlineEquation>-uniformly convergent. We carry out a few numerical experiments to demonstrate the theoretical estimate and show the efficiency of the upwind algorithm on G-mesh in spatial direction over the upwind algorithm on Harmonic and Shishkin meshes in spatial direction.</p>

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A piecewise uniform G-mesh for parabolic interior layer singularly perturbed problems

  • 期刊论文

  • 发表日期：

    2025年2月7日

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  • L. Anitha,
  • M. Prithvi,
  • Kapil K. Sharma,
  • V. P. Ramesh

摘要

In this article, we consider parabolic interior layer singularly perturbed problems and we analyze the problem based on an implicit upwind algorithm on G-mesh in the spatial direction and uniform mesh in the temporal direction. We prove that the error estimate of the algorithm is \(\epsilon\) ϵ -uniformly convergent. We carry out a few numerical experiments to demonstrate the theoretical estimate and show the efficiency of the upwind algorithm on G-mesh in spatial direction over the upwind algorithm on Harmonic and Shishkin meshes in spatial direction.