A quasi-local interpolation operator¶preserving the discrete divergence
A quasi-local interpolation operator¶preserving the discrete divergence
复制标题
DOI：
10.1007/s100920300000
复制
发表时间：
2003-03
期刊：
影响因子：
1.7
通讯作者：
V. Girault;L. R. Scott
中科院分区：
文献类型：
--
作者：
V. Girault;L. R. Scott
我们构造了一个算子，保持离散发散，并具有相同的准局部逼近性质的正则插值，这是非常有用的离散非线性不可压缩流体模型时。对于低次有限元，这种算子有一个显式表达式，可以很容易地导出局部逼近性质。但对于高阶有限元，一般没有显式表达式，这种构造是通过证明一个全局离散inf-sup条件而仅使用局部参数来实现的。我们在协调元和非协调元的一般情况下写出这种构造，然后给出一些应用。
We construct an operator that preserves the discrete divergence and has the same quasi-local approximation properties as a regularizing interpolant; this is very useful when discretizing nonlinear incompressible fluid models. For low-degree finite elements, such operators have an explicit expression, from which local approximation properties can be easily derived. But for higher-degree finite elements, an explicit expression is generally not available and this construction is achieved by proving a global discrete inf–sup condition while using only local arguments. We write this construction in a general case, for conforming and non-conforming elements, and then give some applications.