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Convergence of an adaptive mixed finite element method for convection-diffusion-reaction equations

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Abstract

We prove the convergence of an adaptive mixed finite element method (AMFEM) for (nonsymmetric) convection-diffusion-reaction equations. The convergence result holds for the cases where convection or reaction is not present in convection- or reaction-dominated problems. A novel technique of analysis is developed by using the superconvergence of the scalar displacement variable instead of the quasi-orthogonality for the stress and displacement variables, and without marking the oscillation dependent on discrete solutions and data. We show that AMFEM is a contraction of the error of the stress and displacement variables plus some quantity. Numerical experiments confirm the theoretical results.

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Authors and Affiliations

  1. School of Science, Chongqing Jiaotong University, Chongqing, 400074, China

    ShaoHong Du

  2. Beijing Computational Science Research Center, Beijing, 100084, China

    ShaoHong Du

  3. School of Mathematics, Sichuan University, Chengdu, 610064, China

    XiaoPing Xie

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  1. ShaoHong Du
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  2. XiaoPing Xie
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Du, S., Xie, X. Convergence of an adaptive mixed finite element method for convection-diffusion-reaction equations. Sci. China Math. 58, 1327–1348 (2015). https://doi.org/10.1007/s11425-015-4992-6

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  • DOI: https://doi.org/10.1007/s11425-015-4992-6

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