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Multiquadrics – a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations. (English) Zbl 0850.76048


MSC:

76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
76M99 Basic methods in fluid mechanics
65Z05 Applications to the sciences

Citations:

Zbl 0692.76003
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Full Text: DOI

References:

[1] Kansa, E. J., Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics—I. Surface approximations and partial derivative estimates, Computers Math. Applic., 19, 8/9, 127-145 (1990) · Zbl 0692.76003
[2] Franke, R., Scattered data interpolation: test of some other methods, Math. Comput., 38, 181-200 (1982) · Zbl 0476.65005
[3] R. L. Hardy, Multiquadric equations of topography and other irregular surfaces. J. geophys. Res.176,; R. L. Hardy, Multiquadric equations of topography and other irregular surfaces. J. geophys. Res.176,
[4] Hardy, R. L., Research results in the application of multiquadratic equations to surveying and mapping problems, Surv. Mapp., 35, 321-332 (1975)
[5] Stead, S., Estimation of gradients from scattered data, Rocky Mount. J. Math., 14, 265-279 (1984) · Zbl 0558.65009
[6] Micchelli, C. A., Interpolation of scattered data: distance matrices and conditionally positive definite functions, Constr. Approx., 2, 11-22 (1986) · Zbl 0625.41005
[7] W. R. Madych and S. A. Nelson, Multivariate interpolation: a variational theory. J. Approx. Theory Applic.; W. R. Madych and S. A. Nelson, Multivariate interpolation: a variational theory. J. Approx. Theory Applic. · Zbl 0703.41008
[8] Adams, E., (VII Int. Conf. Computational Methods in Water Resources (June 1988), MIT Press: MIT Press Cambridge, Mass)
[9] Kansa, E. J., Highly accurate shock flow calculations with moving grids and mesh refinement, (Vichnevetsky, R.; Vignes, J., Numerical Mathematics and Applications (1986), North Holland: North Holland New York), 311-316 · Zbl 1185.65178
[10] von Neumann, J., (Traub, A. K., John von Neumann, Collected Works, Vol. 6 (1963), MacMillan: MacMillan New York), 219-237
[11] Kansa, E. J., Application of Hardy’s multiquadratic interpolation to hydrodynamics, (Proc. 1986 Simul Conf., Vol. 4 (1986)), 111-117
[12] Braess, D., The contraction number of a multigrid method for solving the Poisson equation, Numer. Math., 37, 387-404 (1981) · Zbl 0461.65078
[13] Braess, D., The convergence rate of a multigrid method relaxation for the Poisson equation with Gauss-Seidel relaxation for the Poisson equation, Math. Comput., 42, 505-519 (1984) · Zbl 0539.65075
[14] Braess, D.; Hackbusch, W., A new convergence proof for the multigrid method including the V-cycle, SIAM Jl numer. Analysis, 20, 967-975 (1983) · Zbl 0521.65079
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