基于亏量校正求解自然对流问题的后验误差估计子

Recovery-Based Error Estimator for the Natural-Convection Problem Based on Defect-Correction Method

摘要:

Abstract: 本文给出NC方程基于亏量校正方法的恢复型误差估计子。我们在亏量步求解人工黏性系数的稳定非线性问题；在校正步通过线性化方程来校正这个残量，在亏量和校正步我们都采用Oceen迭代。考虑应力张量 ，若我们采用最低阶协调速度和压力有限元对 求解离散NC问题，应力张量的有限元逼近 是不连续的分片常数。我们利用超收敛片恢复技巧构造连续空间的量 ，得到了局部恢复型误差估计子 。最后，通过数值实验验证了基于亏量校正方法的恢复型误差估计子是有效的。 This article solves an artificial viscosity stabilized nonlinear problem in the defect step, and corrects the residual by linearized equations in the correction step for a few steps. In both the defect and correction steps, we use the Oseen iterative scheme to solve the discrete nonlinear equations, considering the stress tensor . For the speed and pressure of NC problem, we use the lowest finite element pair . The discrete finite element stress tensor approximation is discontinuous piecewise constant. We obtain the local recovery type error estimator by the convergence recovery technique to construct in continuous space. Finally, the stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations.