We consider a stationary convection–diffusion–reaction model problem in a two- or three-dimensional bounded domain. We approximate this model by a non-stationary problem and propose a numerical method that combines the method of characteristics with an augmented mixed finite element procedure. We show that this scheme has a unique solution. We also derive a residual-based a posteriori error indicator and prove it is reliable and locally efficient. Finally, we provide some numerical experiments that illustrate the performance of the adaptive algorithm.

中文翻译：

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自适应混合有限元结合特征法解决稳态对流-扩散-反应问题

我们考虑二维或三维有界域中的稳态对流扩散反应模型问题。我们通过非平稳问题来近似该模型，并提出了一种将特征方法与增强混合有限元程序相结合的数值方法。我们证明这个方案有一个独特的解决方案。我们还推导了基于残差的后验误差指标，并证明它是可靠的和局部有效的。最后，我们提供了一些数值实验来说明自适应算法的性能。