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A survey of parametrized variational principles and applications to computational mechanics. (English) Zbl 0848.73063

Summary: We describe recent developments in the area of parametrized variational principles (PVPs) and selected applications to finite element computational mechanics. A PVP is a variational principle containing free parameters that have no effect on the Euler-Lagrange equations. The theory of single-field PVPs, based on gauge functions (also known as null Lagrangians), is a subset of the inverse problems of variational calculus that have limited value. The paper describes the recent construction of multifield PVPs in several areas of elasticity and electromagnetics. It then discusses three applications to finite element computational mechanics: the derivation of high-performance finite elements, the development of element-level error indicators, and the construction of finite element templates. The paper concludes with an overview of open research areas.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
78M30 Variational methods applied to problems in optics and electromagnetic theory
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