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<p>We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence, and uniqueness statements of the corresponding variational methods. We also obtain optimal error estimates of the semidiscrete scheme in corresponding Bochner spaces. Finally, we construct a fully discrete scheme through a backward Euler discretization of the time derivative, and prove well-posedness statements for this fully discrete scheme. Our findings show that the mixed approach removes some theoretical impediments to analysis and is numerically easier to implement. We provide numerical simulations for the mixed formulation approach using <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10915_2025_2997_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^0\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>0</mn> </msup> </math></EquationSource> </InlineEquation> finite elements on several domains. Our numerical results confirm that the algorithm has optimal convergence in accordance with the observed theoretical results.</p>

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Conformal Finite Element Methods for Nonlinear Rosenau-Burgers-Biharmonic Models

  • 期刊论文

  • 发表日期：

    2025年7月24日

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  • Ankur,
  • Ram Jiwari,
  • Akil Narayan

摘要

We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence, and uniqueness statements of the corresponding variational methods. We also obtain optimal error estimates of the semidiscrete scheme in corresponding Bochner spaces. Finally, we construct a fully discrete scheme through a backward Euler discretization of the time derivative, and prove well-posedness statements for this fully discrete scheme. Our findings show that the mixed approach removes some theoretical impediments to analysis and is numerically easier to implement. We provide numerical simulations for the mixed formulation approach using \(C^0\) C 0 finite elements on several domains. Our numerical results confirm that the algorithm has optimal convergence in accordance with the observed theoretical results.