A Mixed Finite Element Method for Multi-Cavity Computation in Incompressible Nonlinear Elasticity (Journal of Computational Mathematics, 2019)
A mixed finite element method combining an iso-parametric $Q_2$-$P_1$ element and aniso-parametric $P^+_2$-$P_1$ element is developed for the computation of multiple cavities inincompressible nonlinear elasticity. The method is analytically proved to be locking-freeand convergent, and it is also shown to be numerically accurate and efficient by numericalexperiments. Furthermore, the newly developed accurate method enables us to find aninteresting new bifurcation phenomenon in multi-cavity growth.