On the control volume finite element methods and their applications to multiphase flow
Zhangxin Chen
Networks & Heterogeneous Media 2006, 1(4): 689-706 doi: 10.3934/nhm.2006.1.689
In this paper we systematically review the control volume finite element (CVFE) methods for numerical solutions of second-order partial differential equations. Their relationships to the finite difference and standard (Galerkin) finite element methods are considered. Through their relationship to the finite differences, upstream weighted CVFE methods and the conditions on positive transmissibilities (positive flux linkages) are studied. Through their relationship to the standard finite elements, error estimates for the CVFE are obtained. These estimates are comparable to those for the standard finite element methods using piecewise linear elements. Finally, an application to multiphase flows in porous media is presented.
keywords: error analysis upstream weighting multiphase flow Galerkin finite element numerical experiments. Control volume finite element
Locking-free nonconforming finite elements for planar linear elasticity
Zhangxin Chen Qiaoyuan Jiang Yanli Cui
Conference Publications 2005, 2005(Special): 181-189 doi: 10.3934/proc.2005.2005.181
In this paper we introduce a nonconforming finite element method for a planar linear elasticity problem. We show that this nonconforming method is robust in that error estimates generated by it are uniform with respect to one of the Lamé elasticity constants, $\l$; i.e., it is locking-free. Applications to nonconforming $P_1$ and rotated $Q_1$ finite elements are discussed.
keywords: locking free Nonconforming finite elements elasticity.

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