Premium
Analysis of expanded mixed methods for fourth‐order elliptic problems
Author(s) -
Chen Zhangxin
Publication year - 1997
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199709)13:5<483::aid-num3>3.0.co;2-f
Subject(s) - mathematics , partial differential equation , order (exchange) , elliptic partial differential equation , partial derivative , tensor (intrinsic definition) , displacement (psychology) , numerical analysis , mathematical analysis , geometry , psychology , finance , economics , psychotherapist
The recently proposed expanded mixed formulation for numerical solution of second‐order elliptic problems is here extended to fourth‐order elliptic problems. This expanded formulation for the differential problems under consideration differs from the classical formulation in that three variables are treated, i.e., the displacement, the stress, and the moment tensors. It works for the case where the coefficient of the differential equations is small and does not need to be inverted, or for the case in which the stress tensor of the equations does not need to be symmetric. Based on this new formulation, various mixed finite elements for fourth‐order problems are considered; error estimates of quasi‐optimal or optimal order depending upon the mixed elements are derived. Implementation techniques for solving the linear system arising from these expanded mixed methods are discussed, and numerical results are presented. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 483–503, 1997