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<p>In this article, we established the convergence of a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p^{th}\)</EquationSource> </InlineEquation> order <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(( p \ge 1)\)</EquationSource> </InlineEquation> finite element method on an exponentially graded Bakhvalov mesh for a convection-diffusion problem which possesses boundary layer. Almost optimal uniform convergence order is proved by careful selection of Lagrange’s interpolants. Numerical results are obtained to verify the theoretical findings.</p>

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Convergence of a Finite Element Method on an Exponentially Graded Bakhvalov Mesh for Convection-Diffusion Problems Possessing Boundary Layers

  • 期刊论文

  • 发表日期：

    2025年10月13日

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  • Sachin Kumar Sahu,
  • Pramod Chakravarthy Podila

摘要

In this article, we established the convergence of a \(p^{th}\) order \(( p \ge 1)\) finite element method on an exponentially graded Bakhvalov mesh for a convection-diffusion problem which possesses boundary layer. Almost optimal uniform convergence order is proved by careful selection of Lagrange’s interpolants. Numerical results are obtained to verify the theoretical findings.