Morin, Pedro; Nochetto, Ricardo H.; Siebert, Kunibert G. Convergence of adaptive finite element methods. (English) Zbl 1016.65074 SIAM Rev. 44, No. 4, 631-658 (2002). The authors consider the use of adaptive finite element methods. They construct an algorithm, which converges linearly and which does not involve preliminary mesh adaptation. They give the results of a number of numerical experiments and point out the possibilities associated with higher order elements and saddle point problems are also discussed. The theory is illustrated a number of diagrams. Reviewer: Ll.G.Chambers (Bangor) Cited in 2 ReviewsCited in 175 Documents MSC: 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 35Q30 Navier-Stokes equations 65Y20 Complexity and performance of numerical algorithms 65N15 Error bounds for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs Keywords:a posteriori error estimators; data oscillation; adaptive mesh refinement; convergence; Stokes problem; Uzawa iterations; adaptive finite element methods; algorithm; numerical experiments; saddle point problems PDFBibTeX XMLCite \textit{P. Morin} et al., SIAM Rev. 44, No. 4, 631--658 (2002; Zbl 1016.65074) Full Text: DOI