The convergence of the cascadic conjugate-gradient method applied to elliptic problems in domains with re-entrant corners

Abstract. We study the convergence properties of the cascadic conjugategradient method (CCG-method), which can be considered as a multilevel method without coarse-grid correction. Nevertheless, the CCG-method converges with a rate that is independent of the number of unknowns and the number of grid levels. We prove this property for two-dimensional elliptic second-order Dirichlet problems in a polygonal domain with an interior angle greater than . For piecewise linear finite elements we construct special nested triangulations that satisfy the conditions of a "triangulation of type (h, , L)" in the sense of I. Babuska, R. B. Kellogg and J. Pitk

• Type: Journal
• Year: 2000
• Where: MOC
• Authors: Vladimir Shaidurov, Lutz Tobiska
• Keywords: Cascadic Conjugategradient Method, Elliptic Second-order Dirichlet, MOC 2000, Polygonal Domain