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A two‐stage least‐squares finite element method for the stress‐pressure‐displacement elasticity equations
Author(s) -
Yang SuhYuh,
Chang Ching L.
Publication year - 1998
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(199805)14:3<297::aid-num2>3.0.co;2-h
Subject(s) - mathematics , finite element method , elasticity (physics) , mathematical analysis , compressibility , norm (philosophy) , least squares function approximation , mixed finite element method , displacement (psychology) , linear elasticity , convergence (economics) , boundary value problem , mechanics , psychology , statistics , materials science , physics , estimator , political science , law , economics , composite material , psychotherapist , thermodynamics , economic growth
A new stress‐pressure‐displacement formulation for the planar elasticity equations is proposed by introducing the auxiliary variables, stresses, and pressure. The resulting first‐order system involves a nonnegative parameter that measures the material compressibility for the elastic body. A two‐stage least‐squares finite element procedure is introduced for approximating the solution to this system with appropriate boundary conditions. It is shown that the two‐stage least‐squares scheme is stable and, with respect to the order of approximation for smooth exact solutions, the rates of convergence of the approximations for all the unknowns are optimal both in the H 1 ‐norm and in the L 2 ‐norm. Numerical experiments with various values of the parameter are examined, which demonstrate the theoretical estimates. Among other things, computational results indicate that the behavior of convergence is uniform in the nonnegative parameter. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 297–315, 1998