Multigrid convergence for nonsymmetric, indefinite variational problems on one smoothing step
Applied Mathematics and Computation - Second Copper Mountain conference on Multigrid methods Copper Mountain, Colorado
The fast adaptive composite grid (FAC) method for elliptic equation
Mathematics of Computation
Local mesh refinement multilevel techniques
SIAM Journal on Scientific and Statistical Computing
Optimal multilevel iterative methods for adaptive grids
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
Domain decomposition algorithms for indefinite elliptic problems
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
A new class of iterative methods for nonselfadjoint or indefinite problems
SIAM Journal on Numerical Analysis
Convergence analysis of multigrid algorithms for nonselfadjoint and indefinite elliptic problems
SIAM Journal on Numerical Analysis
Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems
SIAM Journal on Numerical Analysis
Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problems
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Some new error estimates for Ritz-Galerkin methods with minimal regularity assumptions
Mathematics of Computation
Iterative methods for large, sparse, nonsymmetric systems of linear equations
Iterative methods for large, sparse, nonsymmetric systems of linear equations
Robust A Posteriori Error Estimates for Stationary Convection-Diffusion Equations
SIAM Journal on Numerical Analysis
Convergence of Adaptive Finite Element Methods for General Second Order Linear Elliptic PDEs
SIAM Journal on Numerical Analysis
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In this paper, we propose some local multilevel algorithms for solving linear systems arising from adaptive finite element approximations of nonsymmetric and indefinite elliptic boundary value problems. Two types of local smoothers are constructed. One is based on the original nonsymmetric problems, and the other is defined in terms of the associated symmetric problems. It is shown that the local multilevel methods for the nonsymmetric and indefinite elliptic boundary value problems are optimal, which means that the convergence rates of the local multilevel methods are independent of mesh sizes and mesh levels provided that the coarsest grid is sufficiently fine. Numerical experiments are reported to confirm our theory.