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Linear finite element methods for planar linear elasticity

Authors: Susanne C. Brenner and Li-Yeng Sung
Journal: Math. Comp. 59 (1992), 321-338
MSC: Primary 73V05; Secondary 65N12, 65N30
MathSciNet review: 1140646
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Abstract: A linear nonconforming (conforming) displacement finite element method for the pure displacement (pure traction) problem in two-dimensional linear elasticity for a homogeneous isotropic elastic material is considered. In the case of a convex polygonal configuration domain, $ \mathcal{O}(h)\;(\mathcal{O}({h^2}))$ error estimates in the energy $ ({L^2})$ norm are obtained. The convergence rate does not deteriorate for nearly incompressible material. Furthermore, the convergence analysis does not rely on the theory of saddle point problems.

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Keywords: Linear finite elements, linear elasticity
Article copyright: © Copyright 1992 American Mathematical Society

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