论文标题
耦合统一的Stokes-Brinkman/运输模型的亚网格多尺度稳定有限元法的Apriori和Aposteriori误差估计
Apriori and aposteriori error estimation of Subgrid multiscale stabilized finite element method for coupled unified Stokes-Brinkman/Transport model
论文作者
论文摘要
在这项研究中，我们为完全统一的Stokes-Brinkman问题提供了稳定的有限元分析，并与可变系数的瞬态对流 - 扩散反应方程（VADR）完全结合在一起。同样，我们对Stokes-Brinkman模型进行了稳定的有限元分析，其界面条件与VADR完全耦合。与流量问题有关的流体的粘度取决于溶质的浓度，溶质的传输用VADR方程描述。已采用代数亚网格多尺度方法来达到稳定的耦合变异配方。在离散化的时间里，已经使用了完全隐式的Euler方案。已经提出了稳定子网格多尺度有限元方案的APRIORI和Aposteriori估计值的详细推导。很少进行数值实验来验证该方法的可信度。
In this study, we present a stabilized finite element analysis for completely unified Stokes-Brinkman problems fully coupled with variable coefficient transient Advection-Diffusion-Reaction equation(VADR). As well we have carried out the stabilized finite element analysis for Stokes-Brinkman model with interface conditions fully coupled with VADR. The viscosity of the fluid, involved in flow problem, depends on the concentration of the solute, whose transport is described by VADR equation. The algebraic subgrid multiscale approach has been employed to arrive at the stabilized coupled variational formulation. For the time discretization the fully implicit Euler scheme has been used. A detailed derivation of both the apriori and aposteriori estimates for the stabilized subgrid multiscale finite element scheme have been presented. Few numerical experiments have been carried out to verify the credibility of the method.
