Summary
We propose a multidomain spectral collocation scheme for the approximation of the two-dimensional Stokes problem. We show that the discrete velocity vector field is exactly divergence-free and we prove error estimates both for the velocity and the pressure.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adams, R.A.: Sobolev spaces. San Francisco London: Academic Press 1975
Bernardi, C., Maday, Y.: Relèvement pôlynomial de traces et applications.M 2 AN 24, 1990
Bernardi, C., Maday, Y.: Nonconforming spectral element methods, analysis of some projection operators. J. Appl. Numer. Math.6 (1989/90), 33–52, North Holland
Bernardi, C., Maday, Y., Métivet, B.: Calcul de la pression dans la résolution spectrale du système de Stokes. La Recherche Aérospatiale1, 1–24 (1986)
Brezzi, F.: On the existence, uniqueness and approximation of a saddle point problem arising from Lagrange multipliers. RAIRO Anal. Numer.8, 129–151 (1974)
Canuto, C., Funaro, D.: The Schwarz algorithm for spectral methods. SIAM J. Numer. Anal.25, 24–40 (1988)
Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral methods in fluid dynamics. Berlin Heidelberg New York: Springer 1987
Canuto, C., Pietra, P.: Boundary and interface conditions within a finite element preconditioner for the spectral collocation method. J. Comput. Phys. 1988 (to appear)
Davis, P.J., Rabinowitz, P.: Methods of numerical integration. New York: Academic Press 1975
Funaro, D.: A multidomain spectral approximation of elliptic problems. Numer. Math. for PDE,2, 187–205 (1986)
Funaro, D., Quarteroni, A., Zanolli, P.: An iterative procedure with interface relaxation for domain decomposition methods. SIAM J. Numer. Anal.25, 6 (1988)
Girault, V., Raviart, P.A.: Finite element approximation of Navier-Stokes equations. Theory and algorithms. Berlin Heidelberg New York: Springer 1986
Gottlieb, D., Orszag, S.A.: Numerical analysis of spectral methods. SIAM, Philadelphia 1977
Glowinski, R., Wheeler, M.F.: In domain decomposition methods for partial differential equations. In: Glowinski, R., Golub, G.H., Periaux, J. SIAM, Philadelphia 1987
Maday, Y., Patera, A.T.: Spectral element methods for the incompressible Navier-Stokes equations. In: Noor, A. (ed.) State of the art surveys in computational mechanics. ASME 1989
Marini, D., Quarteroni, A.: A relaxation procedure for domain decomposition using finite elements. Numer. Math.55, 575–598 (1989)
Métivet, B.: Résolution spectrale des équations de Navier-Stokes par une méthode de sousdomaines courbes. Thèse. Univ. Paris VI 1987
Morchoisne, Y.: Résolution des équations de Navier-Stokes par une méthode spectrale de sons-domaines. Comptes-Rendus du 3eme Congrès International sur les Méthodes Numériques de l'Ingénieur. publié par P. Lascaux, Paris 1983
Quarterom, A., Sacchi Landriani, G.: Domain decomposition preconditioners for the spectral collocation method. J. Scient. Comput. 1988 (to appear)
Quarteroni, A., Sacchi Landriani, G.: Parallel algorithm for the capacitance matrix method in domain decomposition. Calcolo1–2, 75–102 (1988)
Vandeven, H.: On the weakly spurious modes in a collocation method for the stokes problem.M 2 AN 23, 649–688 (1989)
Temam, R.: Navier-Stokes equations. Amsterdam: North-Holland 1977
Author information
Authors and Affiliations
Additional information
Deceased
Rights and permissions
About this article
Cite this article
Sacchi Landriani, G., Vandeven, H. A multidomain spectral collocation method for the Stokes problem. Numer. Math. 58, 441–464 (1990). https://doi.org/10.1007/BF01385635
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01385635