An h-adaptive mortar finite element method for finite deformation contact with higher order p extension

In this work we present a generalization of the mortar segment-to-segment method for finite deformations contact to an h-adaptive version with possible p extension, i.e. using higher order approximation. We recall the main ideas of the mortar algorithm and present the key aspects of adaptivity: error estimation and an h-adaptive strategy. The p extension exploits the feature of the hp-adaptive code in which the contact solver is implemented to handle meshes with nodes of nonuniform orders. We use it to set interior nodes to higher order while leaving linear boundary contact nodes which can be processed by the standard mortar algorithm. Accuracy of elements with low order nodes is restored by adequate subdividing of these elements. Adaptivity and p extension are illustrated with a few numerical tests.