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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A Banach spaces-based analysis of a new mixed-primal finite element method for a coupled flow-transport problem
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A Banach spaces-based analysis of a new mixed-primal finite element method for a coupled flow-transport problem

机译：基于Banach空间的耦合流量问题的新混合原始有限元方法分析

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In this paper we introduce and analyze a new finite element method for a strongly coupled flow and transport problem in R-n, n is an element of {2, 3}, whose governing equations are given by a scalar nonlinear convection-diffusion equation coupled with the Stokes equations. The variational formulation for this model is obtained by applying a suitable dual-mixed method for the Stokes system and the usual primal procedure for the transport equation. 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 solvability analysis, which constitutes the main advantage of the present approach. The resulting continuous and discrete schemes, which involve the Cauchy fluid stress, the velocity of the fluid, and the concentration as the only unknowns, are then equivalently reformulated as fixed point operator equations. Consequently, the well-known Schauder, Banach, and Brouwer theorems, combined with BabuSka-Brezzi's theory in Banach spaces, monotone operator theory, regularity assumptions, and Sobolev imbedding theorems, allow to establish the corresponding well-posedness of them. In particular, Raviart-Thomas approximations of order k = 0 for the stress, discontinuous piecewise polynomials of degree = k for the velocity, and continuous piecewise polynomials of degree = k + 1 for the concentration, becomes a feasible choice for the Galerkin scheme. Next, suitable Strang-type lemmas are employed to derive optimal a priori error estimates. Finally, several numerical results illustrating the performance of the mixed-primal scheme and confirming the theoretical rates of convergence, are provided. (C) 2020 Elsevier B.V. All rights reserved.
机译：在本文中，我们介绍并分析RN中的强耦合的流动和运输问题的新有限元方法，n是{2,3}的元素，其控制方程由耦合的标量非线性对流 - 扩散方程给出Stokes方程式。该模型的变分制剂是通过对STOKES系统的合适的双混合方法和运输方程的通常原始程序应用而获得。以这种方式，与以前为此和相关的耦合问题开发的技术不同，现在不需要增强程序进入可解性分析，这构成了本方法的主要优点。然后，涉及Cauchy流体应力，流体速度的连续和离散方案，然后等同地重新重新重新重新重新重新重新重新重新重新重新重新重新重新重新携带Cauchy流体应力，流体的速度，以及浓度。因此，众所周知的Schauder，Banach和Brouwer定理，结合Babuska-Brezzi的理论，在Banach Spaces，单调的操作员理论，规律假设和Sobolev嵌入定理中，允许建立它们的相应良好良好。特别地，对于应力，对于应力，对于速度的不连续分段多项式，浓度<= k + 1的连续分段多项式，浓度的较小程度<= k = 0的radiart-thomas = 0。 Galerkin方案。接下来，采用合适的斯特朗型LEMMA来获得最佳的先验误差估计。最后，提供了说明混合原始方案性能并确认理论收敛速率的数值结果。 （c）2020 Elsevier B.v.保留所有权利。

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