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A Mixed Finite Element Method for Fourth Order Partial Differential Equations
Author(s) -
Balasundaram S.,
Bhattacharyya P. K.
Publication year - 1986
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19860661019
Subject(s) - mathematics , finite element method , lagrange multiplier , curvature , partial differential equation , mathematical analysis , deflection (physics) , partial derivative , constant coefficients , dirichlet problem , variable (mathematics) , bending moment , structural engineering , mathematical optimization , geometry , boundary value problem , physics , classical mechanics , engineering
This paper deals with a new mixed finite element solution of the Dirichlet problem of fourth order elliptic linear partial differential operators with variable coefficients. As examples, bending problems of elastic plates having variable thickness have been considered, for which the algorithm of this method allows a simultaneous determination of the deflection, the curvature components and the „actual” bending and twisting moments of the plate, the „actual” bending and twisting moments being the components of the Lagrange multiplier of this method. Suitable error estimates are obtained under necessary regularity assumptions on the solution.