On the domain geometry dependence of the LBB condition
On the domain geometry dependence of the LBB condition
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DOI：
10.1051/m2an:2000110
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发表时间：
2000-09-01
期刊：
影响因子：
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通讯作者：
Olshanskii, MA
中科院分区：
文献类型：
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作者：
Chizhonkov, EV;Olshanskii, MA
在不可压缩流体计算中，LBB条件是保证有限元（FE）速度-压力对稳定性的重要条件。为保证条件的满足，必须有一个正的、与网格无关的常数。本文研究了LBB条件对区域几何的依赖性。对于模型域，如带和环的几何纵横比，观察到这个常数的实质性依赖。在具有高度各向异性子结构的域中，这可能需要特别注意数值，以防止类似于违反LBB条件时的a-空隙失效。在本文的核心，我们证明了任何FE速度-压力对满足通常的近似假设的LBB条件的网格无关的限制是不大于其连续的对应，从Nei不等式常数。对于后者的显式和渐近准确的估计证明。分析结果通过几个数值实验进行了说明。
The LBB condition is well-known to guarantee the stability of a finite element (FE) velocity - pressure pair in incompressible how calculations. To ensure the condition to be satisfied a certain constant should be positive and mesh-independent. The paper studies the dependence of the LBB condition on the domain geometry. For model domains such as strips and rings the substantial dependence of this constant on geometry aspect ratios is observed. In domains with highly anisotropic substructures this may require special care with numerics to a-void failures similar to those when the LBB condition is violated. In the core of the paper we prove that for any FE velocity-pressure pair satisfying usual approximation hypotheses the mesh-independent limit in the LBB condition is not greater than its continuous counterpart, the constant from the Nei as inequality. For the latter the explicit and asymptotically accurate estimates are proved. The analytic results are illustrated by several numerical experiments.