NUMERICAL SOLUTION OF NONLINEAR ELASTICITY PROBLEMS WITH LAVRENTIEV PHENOMENON

摘要

A convergence theory is established for a truncation method in solving polyconvex elasticity problems involving the Lavrentiev phenomenon. Numerical results on a recent example by Foss et al., which has a polyconvex integrand and admits continuous singular minimizers, not only verify our convergence theorems but also provide a sharper estimate on the upper bound of a perturbation parameter for the existence of the Lavrentiev phenomenon in the example.