• 论文 •

### 离散分解性质和混合元的敛速估计

1. 中国航空研究院计算研究所
• 出版日期:1984-03-14 发布日期:1984-03-14

### GRID DECOMPOSITION PROPERTY AND ERROR ESTIMATES FOR MIXED FINITE ELEMENT METHODS

1. Zhou Tian-xiao Computing Institute, Chinese Aeronautical Establishment
• Online:1984-03-14 Published:1984-03-14

In the paper, the role of GDP (Grid Decomposition Property, introduced in [4])played in the convergence analysis of mixed methods is discussed in connection withthe unified theory developed in [6]. It is pointed out that not GDP, but the gene-ralized Allmann-Johnson condition, plays a crucial role in achieving the optimal errorbounds, nevertheless GDP is important and sufficient for the Babuska-Brezzi condi-tion. The optimal error estimates in [4] are achieved by using two mesh-dependentnorms.
()
 [1] I. Babuska, J. T. Oden, J. K. Lee, Mixed hybrid finite element approximation of second order elliptic boundary value problems, Comput. Methods Appl. Mech. Engrg. 14 (1978) , 1-23． [2] F. Brezzi, On the existence, uniqueness and application of saddle point problems arising from lagrange multipliers, R. A. I. R. O., 8 (1975) , 129-150． [3] P. G. Ciarlet, The Finite Element Method for Elliptic problems, Amsterdam, North Holland Publishing 1977． [4] G. J. Fix, M. D. Gunzburger, R. A. Nicolaides, On mixed finite element methods for first order elliptic systems, Numer. Math., 37 (1981) , 29-48． [5] P. A. Raviart, J. M. Thomas, A mixed finite element method for second order elliptic problems, Methematical aspects of F. E. Ms, Rome, 1975: Lecture Notes in Mathematics, Springer. [6] 周天孝, Equivalency theorem for "saddle-point" finite element schemes and two criteria of strong Babuska-Brezzi condition, Scientia Sinica, 24 (1981) , 1190-1206． [7] 周天孝, Xixed Stiffness model and a unified approach to dual saddle-point finite element Methods in Proceedings of Finite Element Method international invitational Symposium, Heifi, China, 1981． [8] M. Bercovier, O. Pironneau, Error estimates for finite element method solution of the Stokes problem in the primitive variables, Numer. Mith. 33 (1979) , 211-224． [9] R. S. Falk, J. E. Osborn, R. A. I. R. O. Numer. Anal. 14(1980) , 249-277． [10] R. Glowinski, O. Pironneau, On a mixed finite element approximation of the Stokes Problem (Ⅰ), Numer. Math., 33 (1979) , 397-424． [11] C. Johnson, On the convergence of a mixed finite element method for plate bending problems. Numer. Math., 21 (1973) , 43-62． [12] C. Johnson, B. Mercier, Some equilibrium finite element methods for two-dimensional elasticity problems, Numer. Math., 30 (1977) , 103-116． [13] C. Johnson, B. Mercier, Some equilibrium finite element methods for two-dimensional problems in Continuum Mechanics, in "Energy methods in finite element analysis", R. Glowinski, E. Y. Rodin, O. C. Zienkiewicz, Eds. John Wiley and Sons, 1979．
 No related articles found!