论文标题
关于混合有限元配方的INF-SUP条件的必要性
On the necessity of the inf-sup condition for a mixed finite element formulation
论文作者
论文摘要
我们研究了泊松问题的非标准混合配方，有时称为双重混合配方。出于与通量平衡有关的原因，我们使用在h（div）中符合梯度的有限元素，即使该配方允许不连续的有限元元素。该方案不是均匀的INF-SUP稳定，但是我们可以显示解决方案的存在和唯一性，以及在做出合适的规律性假设时，梯度变量的最佳误差估计值。纸上的其他一些言论完成了纸张，对混合配方的不稳定性来源揭示了一些启示。
We study a non standard mixed formulation of the Poisson problem, sometimes known as dual mixed formulation. For reasons related to the equilibration of the flux, we use finite elements that are conforming in H(div) for the approximation of the gradients, even if the formulation would allow for discontinuous finite elements. The scheme is not uniformly inf-sup stable, but we can show existence and uniqueness of the solution, as well as optimal error estimates for the gradient variable when suitable regularity assumptions are made. Several additional remarks complete the paper, shedding some light on the sources of instability for mixed formulations.
