Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
SIAM Journal on Scientific Computing
Inexact and preconditioned Uzawa algorithms for saddle point problems
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
An efficient smoother for the Stokes problem
Applied Numerical Mathematics - Special issue on multilevel methods
Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
SIAM Journal on Numerical Analysis
Multigrid Method for Maxwell's Equations
SIAM Journal on Numerical Analysis
Discrete compactness and the approximation of Maxwell's equations in R3
Mathematics of Computation
Analysis of iterative methods for saddle point problems: a unified approach
Mathematics of Computation
Crouzeix-Velte decompositions for higher-order finite elements
Computers & Mathematics with Applications
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We explore the prospects of utilizing the decomposition of the function space (Ho)' (where n = 2, 3) into three orthogonal subspaces (as introduced by Velte) for the iterative solution of the Stokes -problem It is shown that Uzawa and Arrow-Hurwitz iterations - after at most two initial steps - can proceed fully in the third, smallest subspace. For both methods, we also compute optimal iteration parameters Here, for two-dimensional problems, the lower estimate of the inf-sup constant by Horgan and Payne proves useful and provides an inclusion of the spectrum of the Schur complement operator of the Stokes problem. We further consider the conjugate gradient method in the third Velte subspace and derive a corresponding convergence estimate. Computational results show the effectiveness of this approach for discretizations which admit a discrete Velte decomposition.