A meshing strategy for a quadratic iso-parametric FEM in cavitation computation in nonlinear elasticity

The approximation properties of a quadratic iso-parametric finite element method for a typical cavitation problem in nonlinear elasticity in two dimensions are analyzed. More precisely, (1) the finite element interpolation errors are established in terms of the mesh parameters; (2) a mesh distribution strategy based on an error equi-distribution principle is given; (3) the convergence of finite element cavity solutions is proved. Numerical experiments show that, in fact, the optimal convergence rate can be achieved by the numerical cavity solutions.