Duality estimates and multigrid analysis for saddle point problems arising from mortar discretizations. (English) Zbl 1045.65112

Wieners, Christian; Wohlmuth, Barbara I.

SIAM J. Sci. Comput. 24, No. 6, 2163-2184 (2003).

The authors give an abstract framework for the analysis of multigrid methods for a saddle point problem arising from mortar finite element discretizaitons. The presented approach covers the case of nonnested Lagrange multiplier spaces, and has an advantage that the iterates do not have to be in the positive definite subspace. The multigrid method is applied to different mortar settings including dual Lagrange multipliers, linear elasticity and a rotating geometry. Numerical results demonstrate the flexibility, efficiency and reliability of the presented multigrid method.

Reviewer: Jialin Hong (Beijing)

MSC:

65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs
74B05	Classical linear elasticity
74S05	Finite element methods applied to problems in solid mechanics
35J25	Boundary value problems for second-order elliptic equations

Keywords:

mortar finite elements; nonconforming finite elements; dual estimates; multigrid methods; saddle point problems; Lagrange multiplier; linear elasticity; numerical results

Software:

UG