2 . using the property of the bilinear and trilinear form , a priori bound for solutions of a weak formulation is given 利用雙線性函數和三線性函數的性質,論述了各子問題的有界性、強制性以及解的先驗估計。
In view of the model problem , we do some analysis for the approximations respectively ; we compare uh with the standard finite element approximation of u in vh , and ph with the usual ( non - least - squares ) mixed finite element approximation of p , provided of course that the same approximating spaces are used . it turns out that under weak conditions , they are " almost " equal , i . e . , higher order perturbations of each other . apart from improved a priori bounds , the result also gives us the possibility to extend superconvergence results from the standard and mixed method to the least - squares mixed method 針對模型問題,我們引進對偶問題進行收斂性分析,最小二乘混合元解u _ h與標準有限元解比較,而p _ h則與通常意義下的混合元解比較,結果證明在比較弱的正則性假設條件下,最小二乘混合有限元解u _ h , p _ h標準有限元解u _ h ~ s和混合元解p _ h ~ m的高階擾動。