TY - GEN A1 - Bornemann, Folkmar A. A1 - Krause, Rolf T1 - Classical and Cascadic Multigrid - A Methodical Comparison N2 - Using the full multigrid method {\em without} any coarse grid correction steps but with an a posteriori control of the number of smoothing iterations was shown by Bornemann and Deuflhard [1996] to be an optimal iteration method with respect to the energy norm. They named this new kind of multigrid iteration the {\em cascadic multigrid method}. However, numerical examples with {\em linear} finite elements raised serious doubts whether the cascadic multigrid method can be made optimal with respect to the {\em $L^2$-norm}. In this paper we prove that the cascadic multigrid method cannot be optimal for linear finite elements and show that the case might be different for higher order elements. We present a careful analysis of the two grid variant of the cascadic multigrid method providing a setting where one can understand the methodical difference between the cascadic multigrid method and the classical multigrid $V$-cycle almost immediately. As a rule of thumb we get that whenever the cascadic multigrid works the classical multigrid will work too but not vice versa. T3 - ZIB-Report - SC-96-25 Y1 - 1996 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/236 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-2368 ER -