On a BPX-preconditioner for P1 elements. (English) Zbl 0787.65018

An optimal multilevel preconditioner for nonconforming P1 elements discretizations of second order elliptic boundary value problems is derived. The resulting condition numbers are uniformly bounded with respect to the number of levels \(j\) which is known for the conforming case, and improve the previous results for nonconforming P1 elements.


65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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