An augmented Lagrangian quasi‐Newton solver for constrained nonlinear finite element applications

A solution scheme is presented for constrained non‐linear equations of evolution that result, for example, from the finite element discretization of mechanical contact problems. The algorithm discussed utilizes a quasi‐Newton non‐linear equation solving strategy, with constraints enforced by an augmented Lagrangian iteration procedure. Through presentation of a simple model problem and its generalization, it is shown that the iterations associated with both the quasi‐Newton algorithm and the augmentation procedure can be interwoven to produce a highly efficient and robust solution strategy.