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<p>The research article deals with 2D parabolic convection dominated space shift problems. We applied a novel approach called the alternating direction implicit (ADI) type splitting operator streamline diffusion finite element method. In ADI-type operator splitting, the multidimensional problem is decomposed into a series of one-dimensional subproblems that are solved sequentially along each spatial direction, significantly reducing computational complexity while maintaining stability and accuracy. Theoretical convergence of the numerical solution is established, and numerical validation is also presented at the end of the article.</p>

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Operator splitting FEM for 2D parabolic convection diffusion shift problems

  • 期刊论文

  • 发表日期：

    2025年4月14日

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  • R. Soundararajan,
  • V. Subburayan

摘要

The research article deals with 2D parabolic convection dominated space shift problems. We applied a novel approach called the alternating direction implicit (ADI) type splitting operator streamline diffusion finite element method. In ADI-type operator splitting, the multidimensional problem is decomposed into a series of one-dimensional subproblems that are solved sequentially along each spatial direction, significantly reducing computational complexity while maintaining stability and accuracy. Theoretical convergence of the numerical solution is established, and numerical validation is also presented at the end of the article.