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<p>In this paper, we propose a conforming virtual element method to approximate the eigenfunctions and eigenvalues of the two-dimensional Oseen eigenvalue problem in its classic velocity-pressure formulation. We employ divergence-conforming virtual element spaces, originally developed for the Stokes equations, to approximate the velocity, and piecewise constant functions for the pressure. Under standard mesh assumptions, we derive a priori error estimates for the proposed method using the compact operator theory. In particular, we provide a rigorous tracking of the constants involved in the analysis, with the aim of having a detailed characterization of the convergence in norm between the solution operators. We report a set of numerical tests to confirm the theoretical results.</p>

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A priori error estimates for a conforming VEM for the Oseen eigenvalue problem

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • Danilo Amigo,
  • Felipe Lepe,
  • Nitesh Verma

摘要

In this paper, we propose a conforming virtual element method to approximate the eigenfunctions and eigenvalues of the two-dimensional Oseen eigenvalue problem in its classic velocity-pressure formulation. We employ divergence-conforming virtual element spaces, originally developed for the Stokes equations, to approximate the velocity, and piecewise constant functions for the pressure. Under standard mesh assumptions, we derive a priori error estimates for the proposed method using the compact operator theory. In particular, we provide a rigorous tracking of the constants involved in the analysis, with the aim of having a detailed characterization of the convergence in norm between the solution operators. We report a set of numerical tests to confirm the theoretical results.