Penalty methods in finite element analysis of fluids and structures

This paper discusses the use of penalty techniques in finite element Galerkin equations. It shows that earlier results relating penalty methods to mixed and Lagrange multiplier methods through the use of reduced-selective numerical integration formulas extend to problems in which there is no extremum principle. It is also shown that penalty techniques can be employed in nonlinear dynamical problems and can lead to the substantial computational benefits arising from the ability to impose constraints without Lagrange multiplier unknowns. But they also may lead to costs involving the illconditioning of certein matrices and the complication of some iterative solution procedures. Nevertheless in many problems the benefits well outweigh the costs. (orig.)