zbMATH — the first resource for mathematics

Numerical solution of nonlinear boundary value problems by variational methods. Applications. (English) Zbl 0575.65123
Proc. Int. Congr. Math., Warszawa 1983, Vol. 2, 1455-1508 (1984).
[For the entire collection see Zbl 0553.00001.]
The paper broadly surveys work done by the author and his collaborators on variational methods applied to nonlinear problems, especially to the Navier Stokes equations, to transonic flow of compressible inviscid fluids and to deformations of hyperelastic materials. The techniques considered are finite elements, continuation, penalty, alternating directions, and augmented Lagrangian methods. For proofs and details, the reader is recommended to see the author [Numerical methods for nonlinear variational problems (1984; Zbl 0536.65054)] and the author and M. Fortin (eds.) [Méthodes de lagrangien augmenté. Applications à la résolution numérique des problèmes aux limites (1982; Zbl 0491.65036)].
Reviewer: G.Stoyan

65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
76H05 Transonic flows
74B20 Nonlinear elasticity