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Locking-free adaptive mixed finite element methods in linear elasticity. (English) Zbl 1004.74068
Summary: Mixed finite element methods such as PEERS (plane elasticity elements with reduced symmetry) or BDMS (Brezzi-Douglas-Marini-Stenberg elements) methods were designed to avoid locking for nearly incompressible materials in plane elasticity. In this paper, we establish a robust adaptime mesh-refining algorithm that is rigorously based on a reliable a posteriori error estimate. Numerical evidence is provided for \(\lambda\)-independence of the constants in a posteriori error bounds and for the efficiency of the proposed adaptive mesh-refining algorithm.

74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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