FINITE-ELEMENT APPROXIMATION OF THE NONSTATIONARY NAVIER-STOKES PROBLEM .1. REGULARITY OF SOLUTIONS AND 2ND-ORDER ERROR-ESTIMATES FOR SPATIAL DISCRETIZATION
FINITE-ELEMENT APPROXIMATION OF THE NONSTATIONARY NAVIER-STOKES PROBLEM .1. REGULARITY OF SOLUTIONS AND 2ND-ORDER ERROR-ESTIMATES FOR SPATIAL DISCRETIZATION
复制标题
DOI：
10.1137/0719018
复制
发表时间：
1982-01-01
影响因子：
2.9
通讯作者：
RANNACHER, R
中科院分区：
文献类型：
--
作者：
HEYWOOD, JG;RANNACHER, R
这是第一部分的工作处理严格的误差分析的有限元解的非定常Navier-Stokes方程。二阶误差估计证明空间离散化，使用符合或crack元素。结果表明，流体一样的行为的近似，即使在大数据的情况下，只要解决方案保持定期。该分析是基于尖锐的先验估计的解决方案，特别是反映其行为作为。它表明，在相应的抛物型问题的误差分析中通常假设的规律性不能现实地假设在Navier-Stokes方程的情况下，因为它取决于数据的非局部相容性条件。这里给出的结果是独立的，这样的兼容性条件，这不能在实践中得到验证。
This is the first part of a work dealing with the rigorous error analysis of finite element solutions of the nonstationary Navier–Stokes equations. Second-order error estimates are proven for spatial discretization, using conforming or nonconforming elements. The results indicate a fluid-like behavior of the approximations, even in the case of large data, so long as the solution remains regular. The analysis is based on sharp a priori estimates for the solution, particularly reflecting its behavior asand as. It is shown that the regularity customarily assumed in the error analysis for corresponding parabolic problems cannot be realistically assumed in the case of the Navier–Stokes equations, as it depends on nonlocal compatibility conditions for the data. The results which are presented here are independent of such compatibility conditions, which cannot be verified in practice.