A SURVEY OF PARAMETRIZED VARIATIONAL-PRINCIPLES AND APPLICATIONS TO COMPUTATIONAL MECHANICS

This survey paper describes recent developments in the area of paramet rized variational principles (PVPs) and selected applications to finit e-element computational mechanics. A PVP is a variational principle co ntaining free parameters that have no effect on the Euler-Lagrange equ ations. The theory of single-field PVPs, based on gauge functions (als o known as null Lagrangians) is a subset of the Inverse Problem of Var iational Calculus that has limited value. On the other hand, multifiel d PVPs are more interesting from theoretical and practical standpoints . Following a tutorial introduction, the paper describes the recent co nstruction of multifield PVPs in several areas of elasticity and elect romagnetics. It then discusses three applications to finite-element co mputational mechanics: the derivation of high-performance finite eleme nts, the development of element-level error indicators, and the constr uction of finite element templates. The paper concludes with an overvi ew of open research areas.