CAJ | 학술논문

本文得到了自然对流问题基于牛顿迭代两重网格算法的残量型后验误差估计。相对于标准有限元一层方法的后验误差估计，牛顿迭代两重网格算法的后验误差估计多了一些额外项。通过研究这些额外项的渐近行为，本文得到了这些额外项在误差估计中所起的作用。对于牛顿迭代两重网格方法的最优粗细网格匹配尺寸，这些额外项的收敛阶不高于离散解的收敛阶。数值算例验证了理论分析结论。
본문득도료자연대류문제기우우돈질대량중망격산법적잔량형후험오차고계。상대우표준유한원일층방법적후험오차고계，우돈질대량중망격산법적후험오차고계다료일사액외항。통과연구저사액외항적점근행위，본문득도료저사액외항재오차고계중소기적작용。대우우돈질대량중망격방법적최우조세망격필배척촌，저사액외항적수렴계불고우리산해적수렴계。수치산례험증료이론분석결론。
This paper presents the a posteriori error estimate of residual for natural convec-tion problem, which is computed by the two level Newton finite element method. The a posteriori error estimate contains additional terms in comparison to the one obtained by the standard one level finite element method. The action of the add-itional terms in the error estimate is investigated by studying their asymptotic behaviour. For optimally scaled meshes between coarse and fine meshes of the two level Newton finite element method, the additional terms are not of higher conver-gence order than the order of the numerical solution. Numerical experiments verify the obtained theory results.