In this paper, we study the numerical approximation of a coupled system of elliptic–parabolic equations posed on two separated spatial scales. The model equations describe the interplay between macroscopic and microscopic pressures in an unsaturated heterogeneous medium with distributed microstructures as they often arise in modeling reactive flow in cementitious-based materials. Besides ensuring the well-posedness of our two-scale model, we design two-scale convergent numerical approximations and prove a priori error estimates for the semidiscrete case. We complement our analysis with simulation results illustrating the expected behaviour of the system.

中文翻译：

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耦合两尺度椭圆-抛物线系统的半离散伽辽金方案：适定性和收敛近似率

在本文中，我们研究了在两个分离的空间尺度上提出的椭圆-抛物线方程耦合系统的数值近似。模型方程描述了具有分布式微观结构的不饱和非均质介质中宏观和微观压力之间的相互作用，因为它们经常出现在模拟水泥基材料中的反应流中。除了确保我们的两尺度模型的适定性外，我们还设计了两尺度收敛数值近似，并证明了半离散情况的先验误差估计。我们用模拟结果补充我们的分析，说明系统的预期行为。