caa a22 4500 378920723 CHVBK 20180305123604.0 cr unu---uuuuu 161128e20041101xx s 000 0 eng 10.1515/1569395042571274 doi (NATIONALLICENCE)gruyter-10.1515/1569395042571274 Multigrid analysis for higher order finite difference scheme [Elektronische Daten] [D. Y. Kwak, J. S. Lee] We introduce and analyze a multigrid algorithm for higher order finite difference schemes for elliptic problems on a nonuniform rectangular mesh. These schemes are presented by 9-point stencils. We prove the V-cycle convergence adopting the theory developed for finite element methods to these schemes. To be more precise, we show that the energy norm of the prolongation operator is less than one and hence obtain the conclusion using the approximation and regularity property as in [2]. In the numerical experiment section, we report contraction numbers, eigenvalues and condition numbers of the multigrid algorithm. The numerical test shows that for higher order schemes the multigrid algorithm converges much faster than for low order schemes. We also test the case of a nonuniform grid with a line smoother which also shows good convergence behavior. Copyright 2004, Walter de Gruyter multigrid methods nationallicence higher order finite difference method nationallicence Kwak D. Y. Department of Mathematics, KAIST, Taejon, Korea, 305-701 aut Lee J. S. Department of Mathematics, KAIST, Taejon, Korea, 305-701 aut Journal of Numerical Mathematics Walter de Gruyter 12/4(2004-11-01), 285-296 1570-2820 12:4<285 2004 12 jnma https://doi.org/10.1515/1569395042571274 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/1569395042571274 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kwak D. Y. Department of Mathematics, KAIST, Taejon, Korea, 305-701 aut NATIONALLICENCE 700 1- Lee J. S. Department of Mathematics, KAIST, Taejon, Korea, 305-701 aut NATIONALLICENCE 773 0- Journal of Numerical Mathematics Walter de Gruyter 12/4(2004-11-01), 285-296 1570-2820 12:4<285 2004 12 jnma CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter