Energy norm analysis of exactly symmetric mixed finite elements for linear elasticity. (English) Zbl 1506.65219
The authors are concerned with a detailed analysis of mixed finite element methods for linear elasticity in a polygonal or polyhedral domain for which the symmetry of the stress tensor is exactly satisfied. First, they reconsider the equations of elasticity in mixed form along with their variational formulation and exactly symmetric mixed FEM. Then they study the numerical stability, a priori error analysis and an a posteriori error analysis by hypercircle theorem for FEM solutions. An a posteriori error analysis which is uniformly valid and robust in the incompressible limit is also provided. Some numerical experiments using FEM library Netgen/NGSolve, are carried out in order to validate the analytical findings.
Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca)
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 74B10 | Linear elasticity with initial stresses |
| 74G15 | Numerical approximation of solutions of equilibrium problems in solid mechanics |
Keywords:
mixed finite element method; linear elasticity; stress tensor; symmetry; a priori error estimates; a posteriori error estimates; incompressible limitReferences:
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