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<p>In this paper, a novel linearized 2-step backward differential formula-finite difference streamline diffusion (BDF2-FDSD) method for nonlinear convection-dominated diffusion equation is developed with the nonconforming quadrilateral modified quasi-Wilson finite element. Firstly, by introducing a time discrete system, the error of the solution is split into the temporal error and the spatial error, and the regularities of the solution of time discrete system are obtained by means of mathematical induction. Then, through some typical characteristics of the modified quasi-Wilson element, the unconditional superclose estimate is rigorously deduced without any restriction between the mesh size <i>h</i> and the time step <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3149_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>, which leads to the superconvergence with the interpolation post-processing technique. At last, two numerical examples are carried out to confirm the theoretical results.</p>

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A novel linearized nonconforming BDF2-FDSD method for nonlinear convection-dominated diffusion equation

  • 期刊论文

  • 发表日期：

    2025年3月22日

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  • Dongyang Shi,
  • He Ma

摘要

In this paper, a novel linearized 2-step backward differential formula-finite difference streamline diffusion (BDF2-FDSD) method for nonlinear convection-dominated diffusion equation is developed with the nonconforming quadrilateral modified quasi-Wilson finite element. Firstly, by introducing a time discrete system, the error of the solution is split into the temporal error and the spatial error, and the regularities of the solution of time discrete system are obtained by means of mathematical induction. Then, through some typical characteristics of the modified quasi-Wilson element, the unconditional superclose estimate is rigorously deduced without any restriction between the mesh size h and the time step \(\tau \) τ , which leads to the superconvergence with the interpolation post-processing technique. At last, two numerical examples are carried out to confirm the theoretical results.