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<p>In the present work, we investigate a class of singularly perturbed convection–diffusion systems with characteristic boundaries in two-dimensional space. A priori estimates for the system are analyzed, encompassing the maximum principle, stability results, and bounds for the solution components. A finite difference scheme is developed with the help of layer-adapted meshes. Based on the discrete maximum norm, the error analysis demonstrates that the order of convergence is <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(O(N^{-1}(\ln N)^2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>N</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mrow> <mo stretchy="false">(</mo> <mo>ln</mo> <mi>N</mi> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> for the Shishkin mesh and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(O(N^{-1})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>N</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> for the Bakhvalov–Shishkin mesh. Finally, the outcomes of the numerical experiments are presented to validate the theoretical results.</p>

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A computational technique for a 2D singularly perturbed convection–diffusion system with characteristic layers

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • Harini Chandrasekaran,
  • Vembu Shanthi

摘要

In the present work, we investigate a class of singularly perturbed convection–diffusion systems with characteristic boundaries in two-dimensional space. A priori estimates for the system are analyzed, encompassing the maximum principle, stability results, and bounds for the solution components. A finite difference scheme is developed with the help of layer-adapted meshes. Based on the discrete maximum norm, the error analysis demonstrates that the order of convergence is \(O(N^{-1}(\ln N)^2)\) O ( N - 1 ( ln N ) 2 ) for the Shishkin mesh and \(O(N^{-1})\) O ( N - 1 ) for the Bakhvalov–Shishkin mesh. Finally, the outcomes of the numerical experiments are presented to validate the theoretical results.