Abstract
Considering that, in the discretization of linear differential operators, one can choose suitable nodes of super-convergence for the evaluation of the residual, we apply this idea to first-order operators associated with the approximation of hyperbolic equations, in order to improve some known implicit schemes.
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REFERENCES
Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A. (1988). Spectral Methods in Fluid Dynamics, Springer Series in Comput. Phys., Springer-Verlag, New York.
Deville, M., and Mund, E. (1991). Finite element preconditioning of collocation schemes for advection-diffusion equations Proc. IMACS Int'l. Symp. Iterative Methods in Linear Algebra, Beauwens, R. and de Groen, P. (eds.), North Holland, Amsterdam, pp. 181–190.
Deville, M., and Mund, E. (1992). Fourier analysis of finite element preconditioned collocation schemes, SIAM J. Sci. Statist. Comput. 13, 596.
Funaro, D. (1987). A preconditioning matrix for the Chebyshev differencing operator, SIAM J. Numer. Anal. 24, 1024–1031.
Funaro, D. (1992). Polynomial Approximation of Differential Equations, Lecture Notes in Physics, Springer-Verlag, Heidelberg.
Funaro, D. (1993). A new scheme for the approximation of advection-diffusion equations by collocation, SIAM J. Numer. Anal. 30(6), 1664–1676.
Funaro, D. (1997). Spectral Elements for Transport-Dominated Equations, in Lecture Notes in Computational Sciences and Engineering m.1, Springer, Heidelberg.
Funaro, D., and Rothman, E. (1989). Preconditioning matrices for the pseudo spectral approximation of first-order operators. In Finite Elements Analysis in Fluids, Chung, T. J., and Karr, G. R. (eds.), UAH Press, Huntsville Alabama, pp. 1458–1463.
Funaro, D., and Russo, A. (1993). Approximation of advection-diffusion problems by a modified Legendre grid. In Finite Elements in Fluids, New Trends and Applications, Morgan, K., Oñate, E., Periaux, J., Peraire, J., and Zienkiewicz, O. C. (eds.), Pineridge Press, pp. 1311–1318.
Gottlieb, D., and Orszag, S. A. (1977). Numerical Analysis of Spectral Methods, Theory and Applications, CBMS-NSF Regional Conf. Series in Appl. Math., SIAM, Philadelphia.
Pinelli, A., Benocci, C., and Deville, M. (1994). Chebyshev pseudo-spectral solution of advection-diffusion equations with mapped finite difference preconditioning, J. Comput. Phys. 112(1), 1–11.
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Funaro, D. Improving the Performances of Implicit Schemes for Hyperbolic Equations. Journal of Scientific Computing 12, 385–394 (1997). https://doi.org/10.1023/A:1025624928964
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DOI: https://doi.org/10.1023/A:1025624928964