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It was shown in Chap. 8 that there are several linear discretizations of convection-diffusion-reaction problems that are monotone or satisfy DMPs. In the convection-dominated regime, however, the numerical solutions are usually quite inaccurate. The intrinsic reason is the multiscale character of the problem in this situation, as discussed in Sect. 2.5 . And a mathematical support is provided by the order barrier presented in Sect. 3.1.3.7 .

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Nonlinear Finite Element Methods for Convection-Diffusion-Reaction Problems: Discretizations Based on Modified Variational Forms

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  • 发表日期：

    2025年

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  • Gabriel R. Barrenechea,
  • Volker John,
  • Petr Knobloch

摘要

It was shown in Chap. 8 that there are several linear discretizations of convection-diffusion-reaction problems that are monotone or satisfy DMPs. In the convection-dominated regime, however, the numerical solutions are usually quite inaccurate. The intrinsic reason is the multiscale character of the problem in this situation, as discussed in Sect. 2.5 . And a mathematical support is provided by the order barrier presented in Sect. 3.1.3.7 .