On stability, convergence and accuracy of bES-FEM and bFS-FEM for nearly incompressible elasticity
Provides rigorous theoretical guarantees for improved finite element methods that address volumetric locking in nearly-incompressible elasticity, a known bottleneck in computational mechanics.
The paper presents a theoretical framework proving stability, convergence, and accuracy of bubble-enriched edge-based and face-based smoothed finite element methods for nearly-incompressible elasticity, demonstrating locking-free and non-oscillatory solutions. Numerical examples validate the reliability.
We present in this paper a rigorous theoretical framework to show stability, convergence and accuracy of improved edge-based and face-based smoothed finite element methods (bESFEM and bFS-FEM) for nearly-incompressible elasticity problems. The crucial idea is that the space of piecewise linear polynomials used for the displacements is enriched with bubble functions on each element, while the pressure is a piecewise constant function. The meshes of triangular or tetrahedral elements required by these methods can be generated automatically. The enrichment induces a softening in the bilinear form allowing the weakened weak (W2)procedure to produce a high-quality solution, free from locking and that does not oscillate. We prove theoretically that both methods confirm the uniform inf-sup and convergence conditions. Four numerical examples are given to validate the reliability of the bES-FEM and bFS-FEM.