Abstract
In this paper a two-grid algorithm is discussed for the mixed finite element discretization of Poisson’s equation. The algorithm is based on a Vanka-type relaxation; the grid transfer operators are selected in accordance with the discretization. Local mode analysis is used to show that Vanka-type relaxation is an efficient smoother indeed. By studying the Fourier transform of the error amplification matrix we find that the canonical grid transfer operators are sufficiently accurate for grid independent convergence. However, this conclusion depends on the relaxation pattern used.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Molenaar, J., and P.W. Hemker (1990). A multigrid approach for the solution of the 2D semiconductor equations, IMPACT, to appear.
Vanka, S.P. (1986). Block-Implicit Multigrid Solution of Navier-Stokes Equations in Primitive Variables, J. Comput. Phys., 65, 138–158.
Polak, S.J. W.H.A. Schilders and H.D. Couperus (1988). A finite element method with current conservation, in Simulation of Semiconductor Devices and Processes, Vol. 3, Bologna, Techno-print.
Brandt, A. (1982). Guide to multigrid development, in Multigrid Methods, Springer Verlag, Lecture Notes in Mathematics 960.
Hemker, P.W. (1990). On the order of prolongations and restrictions in multigrid procedures, J. Appl. Math., to appear.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Basel AG
About this chapter
Cite this chapter
Molenaar, J. (1991). A two-grid analysis of the combination of mixed finite elements and Vanka-type relaxation. In: Hackbusch, W., Trottenberg, U. (eds) Multigrid Methods III. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 98. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5712-3_23
Download citation
DOI: https://doi.org/10.1007/978-3-0348-5712-3_23
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5714-7
Online ISBN: 978-3-0348-5712-3
eBook Packages: Springer Book Archive