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<p>In this paper, we study the a posteriori error estimates of the conforming mixed method for the modified transmission eigenvalue problem proposed by Cogar et al. (Inverse Problems 33: 055010, 2017). We give the a posteriori error estimator of the approximate eigenpair, prove the reliability and efficiency of the estimator for the approximate eigenfunction, and present the reliability of the estimator for the approximate eigenvalue. We also implement adaptive computation and exhibit the numerical experiments which show that the approximate eigenvalues obtained by the adaptive computation reach the optimal convergence order.</p>

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An Adaptive Conforming Mixed Method for the Modified Transmission Eigenvalue Problem for Absorbing Medium

  • 期刊论文

  • 发表日期：

    2025年5月30日

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  • Jinhua Feng,
  • Yanjun Li,
  • Hai Bi,
  • Yidu Yang

摘要

In this paper, we study the a posteriori error estimates of the conforming mixed method for the modified transmission eigenvalue problem proposed by Cogar et al. (Inverse Problems 33: 055010, 2017). We give the a posteriori error estimator of the approximate eigenpair, prove the reliability and efficiency of the estimator for the approximate eigenfunction, and present the reliability of the estimator for the approximate eigenvalue. We also implement adaptive computation and exhibit the numerical experiments which show that the approximate eigenvalues obtained by the adaptive computation reach the optimal convergence order.