论文标题
关于自然对流问题的低阶拉格朗日有限元方法的收敛
On the convergence of a low order Lagrange finite element approach for natural convection problems
论文作者
论文摘要
本文的目的是研究自然对流问题的低阶有限元近似值的收敛性。我们证明，如果在差异方程中与罚款项一起使用，则基于每个变量的P1多项式（速度，压力和温度）基于P1多项式的离散化，以补偿INF-SUP条件的损失。有了对压力规律性的轻度假设，我们恢复了Navier-Stokes-BoussinesQ系统的收敛性，前提是根据网格大小选择罚款项。我们表达条件以获得最佳的收敛顺序。我们用广泛的例子说明了理论收敛结果。还评估了该方法可以节省的计算成本。
The purpose of this article is to study the convergence of a low order finite element approximation for a natural convection problem. We prove that the discretization based on P1 polynomials for every variable (velocity, pressure and temperature) is well-posed if used with a penalty term in the divergence equation, to compensate the loss of an inf-sup condition. With mild assumptions on the pressure regularity, we recover convergence for the Navier-Stokes-Boussinesq system, provided the penalty term is chosen in accordance with the mesh size. We express conditions to obtain optimal order of convergence. We illustrate theoretical convergence results with extensive examples. The computational cost that can be saved by this approach is also assessed.
