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<p>In this paper, an energy dissipative scheme is developed with step-2 backward differential formula(BDF2) finite element method(FEM) for Sobolev equation with Burgers’ type nonlinearity. Based on the energy dissipation behavior, the existence and uniqueness of the numerical solution of the scheme are proved directly. Then the unconditional superclose property and superconvergence result are derived through the high accuracy estimates of the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(P_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-element and interpolated postprocessing approach on anisotropic triangular meshes. Finally, several numerical examples are given to confirm the theoretical analysis.</p>

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Anisotropic unconditional superconvergence analysis of an energy dissipative BDF2-FEM for Sobolev equation with Burgers’ type nonlinearity

  • 期刊论文

  • 发表日期：

    2026年7月4日

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  • Weijun Zhu,
  • Junjun Wang

摘要

In this paper, an energy dissipative scheme is developed with step-2 backward differential formula(BDF2) finite element method(FEM) for Sobolev equation with Burgers’ type nonlinearity. Based on the energy dissipation behavior, the existence and uniqueness of the numerical solution of the scheme are proved directly. Then the unconditional superclose property and superconvergence result are derived through the high accuracy estimates of the \(P_1\) P 1 -element and interpolated postprocessing approach on anisotropic triangular meshes. Finally, several numerical examples are given to confirm the theoretical analysis.