An algebraic study of a local multigrid method for variational problems (Q1200171)

The author presents and analyzes a two-level iterative method for solving systems of equations arising in the process of numerical solution of elliptic variational problems by finite element methods. The method is based on the correction scheme method of \textit{A. Brandt} [Math. Comput. 31, 333-390 (1977; Zbl 0373.65054)]. Essentially, the method is identical to the fast adaptive composite grid method with smoothing on the refined subregion proposed by \textit{S. McCormick} and \textit{J. Thomas} [Math. Comput. 46, 439-456 (1986; Zbl 0594.65078)]. However, the corresponding theory is different. It is an extension of results presented by \textit{A. Brandt} [Appl. Math. Comput. 19, 23-56 (1986; Zbl 0616.65037)] and by the author and \textit{J. Mandel} [ibid. 23, 121-135 (1987; Zbl 0621.73097)].