Abstract
We are interested in the approximation of 2D elliptic equations with dominated advection and featuring boundary layers. In order to reduce the computational complexity, the domain is split into two subregions, the first one far from the layer, where we can neglect the viscosity effects, and the second one next to the layer. In the latter domain the original elliptic equation is solved, while in the former one, the pure convection equation obtained by the original one by dropping the diffusive term is approximated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Y. Achdou. The mortar element method for convection diffusion problems. C.R. Acad. Sci. Paris. Sér. I Math., 321:117–123, 1995.
C. Bernardi, Y. Maday, and A.T. Patera. A new nonconforming approach to domain decomposition: the mortar element method. In Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. XI (Paris, 1989–1991), volume 299 of Pitman Res. Notes Math. Ser., pages 13–51. Longman Sci. Tech., Harlow, 1994.
P.J. Blanco, P. Gervasio, and A. Quarteroni. Extended variational formulation for heterogeneous partial differential equations. Comp. Meth. in Applied Math., 11:141–172, 2011.
C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang. Spectral Methods. Evolution to Complex Geometries and Applications to Fluid Dynamics. Springer, Heidelberg, 2007.
F. Gastaldi, A. Quarteroni, and G. Sacchi Landriani. On the coupling of two dimensional hyperbolic and elliptic equations: analytical and numerical approach. In J.Périeaux T.F.Chan, R.Glowinski and O.B.Widlund, editors, Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, pages 22–63, Philadelphia, 1990. SIAM.
H.A. van der Vorst. Iterative Krylov methods for large linear systems, volume 13 of Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge, 2003.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Blanco, P., Gervasio, P., Quarteroni, A. (2013). Mortar Coupling for Heterogeneous Partial Differential Equations. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_49
Download citation
DOI: https://doi.org/10.1007/978-3-642-35275-1_49
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35274-4
Online ISBN: 978-3-642-35275-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)