Well-conditioned spectral discretizations of the biharmonic operator

References

• Girault , V. and Raviart , P. A. 1979 . Finite Element Approximation of the Navier-Stokes Equations , Berlin : Springer-Verlag .
   Google Scholar
• Gottlieb , D. and Orszag , S. A. 1977 . Numerical Analysis of Spectral Methods: Theory and Applications , Philadelphia : SIAM .
   Google Scholar
• Gregory , R. D. 1980 . The semi-infinite strip x ≥ 0, − 1 ≤ y ≤ 1; completeness of the Papkovich-Fadleeigenfunctions when Φ xx (0y), Φ yy (0y) are prescribed . J. Elasticity , 10 : 57 – 80 .
   Google Scholar
• Heinrichs , W. 1989 . Improved condition number for spectral methods . Math. Comput. , 10 : 103 – 119 .
   Google Scholar
• Joseph , D. D. and Sturges , L. 1975 . The free surface on a liquid filling a trench heated from its side . J. Fluid Mech. , 69 : 565 – 589 .
   Google Scholar
• Karageorghis , A. and Phillips , T. N. 1989 . Spectral collocation methods for Stokes flow in contraction geometries and unbounded domains . J. Comput. Phys. , 80 : 314 – 330 .
   Google Scholar
• Karageorghis , A. and Phillips , T. N. 1991 . Conforming Chebyshev spectral collocation methods for the solution of laminar flow in a constricted channel . IMA J. Numer. Anal , 11 : 33 – 54 .
   Google Scholar
• Nag (UK) Ltd Oxford, UK NAG Library Mark 11, . Banbury Road
   Google Scholar
• Orszag , S. A. 1980 . Spectral methods for problems in complex geometries . J. Comput. Phys. , 37 : 70 – 90 .
   Web of Science ®Google Scholar
• Phillips , T. N. 1989 . Singular matched eigenfunction expansions for Stokes flow around a corner . IMA J. Appl. Math. , 42 : 13 – 26 .
   Google Scholar
• Spence , D. A. 1982 . A note on the eigenfunction expansion for the elastic strip . SIAM J. Appl. Math. , 42 : 155 – 173 .
   Google Scholar
• Smith , R. C. T. 1952 . The bending of a semi-infinite strip . Aust. J. Sci. Res. , 5 : 227 – 237 .
   Google Scholar
• Trogdon , A. A. and Joseph , D. D. 1980 . The stick-slip problem for a round jet . Rheol. Acta , 19 : 404 – 420 .
   Google Scholar
• Trogdon , A. A. and Joseph , D. D. 1982 . Matched eigenfunction expansions for slow flow over a slot . J. Non-Newtonian Fluid Mech. , 10 : 185 – 213 .
   Google Scholar