Douglas, Craig C. Multi-grid algorithms with applications to elliptic boundary-value problems. (English) Zbl 0534.65062 SIAM J. Numer. Anal. 21, 236-254 (1984). This paper extends the multigrid convergence proof by R. E. Bank and T. Dupont [Math. Comput. 36, 35-51 (1981; Zbl 0466.65059)] for symmetric, positive definite problems to the case when the solution spaces need not be nested. The results are applied to self-adjoint elliptic problems discretized by finite elements and finite differences. Reviewer: J.Mandel Cited in 12 Documents MSC: 65N22 Numerical solution of discretized equations for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65F10 Iterative numerical methods for linear systems 35J25 Boundary value problems for second-order elliptic equations Keywords:smoothing iterations; multigrid methods; convergence; finite elements Citations:Zbl 0466.65059 PDFBibTeX XMLCite \textit{C. C. Douglas}, SIAM J. Numer. Anal. 21, 236--254 (1984; Zbl 0534.65062) Full Text: DOI Link