[1] Brezzi F, Fortin M. Mixed and hybrid finite element methods[M]. Springer Science & Business Media, 2012.[2] Scholtz R. A mixed method for fourth-order problems using the linear finite elements[J]. RAIRO Numer. Anal, 1978, 15:85-90.[3] Roberts J E, Thomas J M. Mixed and hybrid methods[J]. Handbook of numerical analysis, 1991, 2:523-639.[4] Bernardi C, Maday Y. Spectral methods[J]. Handbook of numerical analysis, 1997, 5:209-485.[5] Bernardi C, Coppoletta G, Maday Y. Some spectral approximations of two-dimensional fourthorder problems[J]. Mathematics of computation, 1992, 59(199):63-76.[6] Koornwinder T. Two-variable analogues of the classical orthogonal polynomials[J]. Theory and applications of special functions, 1975:435-495.[7] Guo B Y, Shen J, Wang L L. Generalized Jacobi polynomials/functions and their applications[J]. Applied Numerical Mathematics, 2009, 59(5):1011-1028.[8] Mercier B, Osborn J, Rappaz J, et al. Eigenvalue approximation by mixed and hybrid methods[J]. Mathematics of Computation, 1981, 36(154):427-453.[9] Polizzi E. Density-matrix-based algorithm for solving eigenvalue problems[J]. Physical Review B, 2009, 79(11):115112.[10] Guo B, Wang L L. Error analysis of spectral method on a triangle[J]. Advances in Computational Mathematics, 2007, 26(4):473-496.[11] Li H, Shen J. Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle[J]. Mathematics of Computation, 2010, 79(271):1621-1646.[12] Schwab C. p-and hp-finite element methods:Theory and applications in solid and fluid mechanics[M]. Oxford University Press, 1998.[13] Canuto C G, Hussaini M Y, Quarteroni A M, et al. Spectral Methods:Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation)[M]. Springer-Verlag New York, Inc., 2007.[14] Weikun Shan and Huiyuan Li. The triangular spectral element method for Stokes eigenvalues[J]. Math-ematics of Computation, 2016, Accepted.[15] Maz'ya V. Sobolev Spaces:with Applications to Elliptic Partial Differential Equations[J]. 2011.[16] Babuska I, Guo B. Direct and inverse approximation theorems for the p-version of the finite element method in the framework of weighted Besov spaces. part I:Approximability of functions in the weighted Besov spaces[J]. SIAM Journal on Numerical Analysis, 2002, 39(5):1512-1538.[17] Falk R S, Osborn J E. Error estimates for mixed methods[J]. RAIRO-Analyse num W rique, 1980, 14(3):249-277.[18] Boffi D, Brezzi F, Gastaldi L. On the convergence of eigenvalues for mixed formulations[J]. Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 1997, 25(1-2):131-154.[19] Blum H, Rannacher R, Leis R. On the boundary value problem of the biharmonic operator on domains with angular corners[J]. Mathematical Methods in the Applied Sciences, 1980, 2(4):556-581.[20] Grisvard P. Elliptic problems in nonsmooth domains[M]. SIAM, 2011.[21] Gerasimov T, Stylianou A, Sweers G. Corners give problems when decoupling fourth order equations into second order systems[J]. SIAM Journal on Numerical Analysis, 2012, 50(3):1604-1623.[22] Babuška I, Guo B Q. Approximation properties of the h-p version of the finite element method[J]. Computer Methods in Applied Mechanics and Engineering, 1996, 133(3):319-346. |