Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
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
Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
SIAM Journal on Numerical Analysis
Computational scales of Sobolev norms with application to preconditioning
Mathematics of Computation
On the Nonlinear Inexact Uzawa Algorithm for Saddle-Point Problems
SIAM Journal on Numerical Analysis
Data Oscillation and Convergence of Adaptive FEM
SIAM Journal on Numerical Analysis
Adaptive Wavelet Methods for Saddle Point Problems---Optimal Convergence Rates
SIAM Journal on Numerical Analysis
An Adaptive Uzawa FEM for the Stokes Problem: Convergence without the Inf-Sup Condition
SIAM Journal on Numerical Analysis
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
Residual reduction algorithms for nonsymmetric saddle point problems
Journal of Computational and Applied Mathematics
Multilevel discretization of symmetric saddle point systems without the discrete LBB condition
Applied Numerical Mathematics
Multilevel Gradient Uzawa Algorithms for Symmetric Saddle Point Problems
Journal of Scientific Computing
| Hi-index | 7.29 |
For any continuous bilinear form defined on a pair of Hilbert spaces satisfying the compatibility Ladyshenskaya-Babusca-Brezzi condition, symmetric Schur complement operators can be defined on each of the two Hilbert spaces. In this paper, we find bounds for the spectrum of the Schur operators only in terms of the compatibility and continuity constants. In light of the new spectral results for the Schur complements, we review the classical Babusca-Brezzi theory, find sharp stability estimates, and improve a convergence result for the inexact Uzawa algorithm. We prove that for any symmetric saddle point problem, the inexact Uzawa algorithm converges, provided that the inexact process for inverting the residual at each step has the relative error smaller than 1/3. As a consequence, we provide a new type of algorithm for discretizing saddle point problems, which combines the inexact Uzawa iterations with standard a posteriori error analysis and does not require the discrete stability conditions.