A fully-mixed formulation in Banach spaces for the coupling of the steady Brinkman-Forchheimer and double-diffusion equations
A fully-mixed formulation in Banach spaces for the coupling of the steady Brinkman-Forchheimer and double-diffusion equations
复制标题
Banach 空间中用于稳定 Brinkman-Forchheimer 和双扩散方程耦合的完全混合公式
DOI：
--
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
J. Ortega
中科院分区：
文献类型：
--
作者：
Sergio Caucao;G. Gatica;J. Ortega
我们提出并分析了一种新的混合有限元方法，用于解决由稳定 Brinkman-Forchheimer 和双扩散方程耦合给出的非线性问题。除了速度、温度和浓度之外，我们的方法还引入了速度梯度、赝应力张量以及一对涉及温度/浓度、其梯度和速度的向量，作为进一步的未知数。因此，我们获得了一个完全混合的变分公式，在每组方程中呈现出巴纳赫空间框架。这样，与之前针对此问题和相关耦合问题开发的技术不同，现在不需要将增强过程合并到公式中，也不需要合并到可解性分析中。然后将所得的非增广格式等效地写为定点方程，从而应用著名的巴拿赫定理，结合非线性单调算子的经典结果和巴拿赫空间中的Babusska-Brezzi理论，证明连续和离散系统的唯一可解性。指定满足所需离散 inf-sup 条件的适当有限元子空间，并导出最佳先验误差估计。几个数值例子证实了理论收敛率，并说明了该方法的性能和灵活性。
We propose and analyze a new mixed finite element method for the nonlinear problem given by the coupling of the steady Brinkman--Forchheimer and double-diffusion equations. Besides the velocity, temperature, and concentration, our approach introduces the velocity gradient, the pseudostress tensor, and a pair of vectors involving the temperature/concentration, its gradient and the velocity, as further unknowns. As a consequence, we obtain a fully mixed variational formulation presenting a Banach spaces framework in each set of equations. In this way, and differently from the techniques previously developed for this and related coupled problems, no augmentation procedure needs to be incorporated now into the formulation nor into the solvability analysis. The resulting non-augmented scheme is then written equivalently as a fixed-point equation, so that the well-known Banach theorem, combined with classical results on nonlinear monotone operators and the Babusska-Brezzi theory in Banach spaces, are applied to prove the unique solvability of the continuous and discrete systems. Appropriate finite element subspaces satisfying the required discrete inf-sup conditions are specified, and optimal a priori error estimates are derived. Several numerical examples confirm the theoretical rates of convergence and illustrate the performance and flexibility of the method.
裂隙多孔弹性介质中的流动和传输
DOI：
10.1007/s13137-019-0119-5
发表时间：
2019
期刊：
GEM - International Journal on Geomathematics
影响因子：
--
作者：
Ambartsumyan, Ilona;Khattatov, Eldar;Nguyen, Truong;Yotov, Ivan
通讯作者：
Yotov, Ivan