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<p>In two dimensions, we analyze a priori and a posteriori error estimates for a conforming virtual element method, applied to the non-symmetric diffusion-convection eigenvalue problem. The theory is developed under standard assumptions on the polygonal meshes. The analysis of the spectral problem and its approximation is based on the compact operators theory and as a consequence, we conclude that the numerical method is spurious free. We present a series of numerical tests in order to confirm our theoretical findings, particularly on the computation of orders of convergence and the performance of the a posteriori error estimator.</p>

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A priori and a posteriori error analysis for a VEM discretization of the convection–diffusion eigenvalue problem

  • 期刊论文

  • 发表日期：

    2025年7月8日

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  • Danilo Amigo,
  • Felipe Lepe,
  • Gonzalo Rivera

摘要

In two dimensions, we analyze a priori and a posteriori error estimates for a conforming virtual element method, applied to the non-symmetric diffusion-convection eigenvalue problem. The theory is developed under standard assumptions on the polygonal meshes. The analysis of the spectral problem and its approximation is based on the compact operators theory and as a consequence, we conclude that the numerical method is spurious free. We present a series of numerical tests in order to confirm our theoretical findings, particularly on the computation of orders of convergence and the performance of the a posteriori error estimator.