Mixed displacement-rotation-pressure formulations for linear elasticity. (English) Zbl 1440.74457
Summary: We propose a new locking-free family of mixed finite element and finite volume element methods for the approximation of linear elastostatics, formulated in terms of displacement, rotation vector, and pressure. The unique solvability of the three-field continuous formulation, as well as the well-definiteness and stability of the proposed Galerkin and Petrov-Galerkin methods, is established thanks to the Babuška-Brezzi theory. Optimal a priori error estimates are derived using norms robust with respect to the Lamé constants, turning these numerical methods particularly appealing for nearly incompressible materials. We exemplify the accuracy (in a suitably weighted norm), as well the applicability of the new formulation and the mixed schemes by conducting a number of computational tests in 2D and 3D, also including cases not covered by our theoretical analysis.
MSC:
| 74S10 | Finite volume methods applied to problems in solid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 65N08 | Finite volume methods for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 74B05 | Classical linear elasticity |
Keywords:
elasticity equations; rotation vector; mixed finite elements; finite volume element formulation; error analysisReferences:
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