An optimal-order multigrid method for P1 nonconforming finite elements. (English) Zbl 0664.65103

Brenner, Susanne C.

Math. Comput. 52, No. 185, 1-15 (1989).

Dirichlet and von Neumann problems for the elliptic equation \(-\nabla (a\nabla u)+bu=f\) in a convex polygon are approximated by a nonconforming finite element method. Piecewise linear approximations are continuous at the midpoints of the edges of elementary triangles. Modifications of multigrid methods for the corresponding systems of equations are analyzed. Special attention is paid to W-cycle methods and estimates of optimal type are obtained. Generalizations to quadratic nonconforming finite element methods are considered as well.

Reviewer: E.D’yakonov

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10	Iterative numerical methods for linear systems
35J25	Boundary value problems for second-order elliptic equations

Keywords:

nonconforming finite element method; multigrid methods; W-cycle methods