基于非协调元的加法型Schwarz交替法──弱重迭情形

ADDITIVE SCHWARZ ALTERNATING METHOD FORNONCONFORMING FINITE ELEMENT──CASE OF WEAK OVERLAP

基于非协调元的加法型Ｓｃｈｗａｒｚ交替法──弱重迭情形黄建国（上海交通大学应用数学系）ＡＤＤＩＴＩＶＥＳＣＨＷＡＲＺＡＬＴＥＲＮＡＴＩＮＧＭＥＴＨＯＤＦＯＲＮＯＮＣＯＮＦＯＲＭＩＮＧＦＩＮＩＴＥＥＬＥＭＥＮＴ──ＣＡＳＥＯＦＷＥＡＫＯＶＥＲＬＡＰ￥Ｈ...

Abstract In this paper, the author builds a weakly overlapping domain decompositionalgorithm for Grouzeix-Raviat finite element method which is easier to executethan that in [9]. The author prove that the condition number of the algorithmis quasi-optimal, equal to O((1 + logH/h)2) where H, h denote the diameters ofthe coarse triangulatinn and finite elemeat triangulation respectively. In order toget this result, a useful lemma (lemma 3.7) is given which plays an important rolein our research as the extension theorem introduced by Widlund[4] for conformingfinite element domain decomposition methods.