hp‐Version finite elements for geometrically non‐linear problems

A p‐version of the finite element method and an hp‐extension is applied to a geometrically non‐linear model problem. Starting from a standard formulation in finite elasticity, some implementation details are outlined. The robustness and efficiency of this method, as already well known for linear problems, is demonstrated. In two numerical examples high accuracy and exponential rate of convergence in energy are shown. The method presented can be used effectively in problems where standard low‐order plane strain elements fail to give accurate results.