We develop a formal construction of a pointwise divergence-free basis in the nonconforming virtual element method of arbitrary order for the Stokes problem introduced in [19]. The proposed construction can be seen as a generalization of the divergence-free basis in Crouzeix-Raviart finite element space [10, 17] to the virtual element space. Using the divergence-free basis obtained from our construction, we can eliminate the pressure variable from the mixed system and obtain a symmetric positive definite system. Several numerical tests are presented to confirm the efficiency and the accuracy of our construction.
翻译:我们为[19] 引入的斯托克斯问题任意秩序的不符合同的虚拟要素方法制定了一个没有差异的正式基础。提议的构建可被视为将Crouzix-Raviart有限要素空间[10、17]的无差异基础普遍化为虚拟要素空间。利用从构建中获得的无差异基础,我们可以消除混合系统中的压力变量,并获得一个对称正数确定系统。提出了若干数字测试,以确认我们构建的效率和准确性。