Adcroft , A. and Marshall , D. 1998 . How slippery are piecewise constant coastlines in numerical ocean models . Tellus 50A , 95 – 108 .
Babuska , I. 1971 . Error bounds for finite elements methods . Numer. Math . 16 , 322 – 333 .
Beardsley , R. C. 1973 . A numerical model of the wind-driven ocean circulation in a circular basin . Geophys. Fluid Dyn . 4 , 211 – 241 .
Brezzi , E, 1974 . On the existence, uniqueness and approximation of saddle point problems arising from Lagrangian multipliers . RAIRO, Anal. Num . 8 ( R2 ), 129 – 151 .
Briggs , W. L. 1980 . A new class of steady solutions of the barotropic vorticty equation . Dyn. Atmos. Oceans 4 , 67 – 99 .
Cockburn , B. , Hou , S. and Shu , C.-W. 1990 . TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case . Math. Comput . 54 , 545 – 581 .
Davey , M. K. , Hsieh , W. W. and Wajsowicz , R. C. 1983 . The free Kelvin wave with lateral and vertical viscosity . J. Phys. Oceanogr . 13 , 2182 – 2191 .
Dupont , E and Lin , C. A . 2004 . The adaptive spectral element method and comparisons with more traditional formulations for ocean modelling . J. Mar. Atmos. Technol . 21 , 135 – 197 .
Dupont , E , Straub , D. N. and Lin , C. A. 2003 . Influence of a step-like coastline on the basin scale voracity budget of mid-latitude gyre models . Tellus 55A , 255 – 272 .
Gent , P. R. 1993 . The energetically consistent shallow water equations. J. Atmos. Sc i . 50 , 1323 – 1325 .
Harrison , D. E. and Holland , W. R. 1981 . Regional eddy voracity transport and the equilibrium voracity budgets of a numerical model ocean circulation . J. Phys. Oceanogr . 11 , 190 – 208 .
Ierley , G. R. and Sheremet , V. A. 1995 . Multiple solutions and advection-dominated flows in the wind-driven circulation. Part I: slip . J. Mar. Res . 53 , 703 – 738 .
Iskandarani , M. , Haidvogel , D. B. and Boyd , J. P. 1995 . A staggered spectral element model with application to the oceanic shallow water equations . Int. J. Numer. Methods Fluids 20 , 393 – 414 .
Kiss , A. E. 2002. Potential voracity “crisis”, adverse pressure gradient, and western boundary current separation. J. Mar. Res . 60 , 60 – 803 .
Ladyzhenskaya , O. A. 1969 . The Mathematical Theory of Viscous Incompressible Flow . Gordon and Breach , London .
Lomtev , I. and Kamiadakis , G. 1999 . A discontinuous Galerkin method for the Navier-Stokes equations , Int. J. Numer. Methods Fluids 29 , 587 – 603 .
Luyten , J. R. , Pedlosky , J. and Stommel , H. 1983 . The ventilated thermocline , J. Phys. Oceanogr . 13 , 292 – 309 .
Ma , H., 1993 . A spectral element basin model for the shallow water equations . J. Comput. Phys . 109 , 133 – 149 .
Madec , G. , Chortler , M. , Delecluse , P. and Crepon , M. 1991 . A three-dimensional study of deep-water formation in the northwestern mediterranean sea . J. Phys. Oceanogr . 21 , 1349 – 1371 .
Marshall , J. C. 1984. Ed dy mean flow interaction in a barotropic ocean model. Q. J. R. Meteorol. Soc . 110 , 110 – 590 .
Mavriplis , C. and Hsu , L.-C. 1997 . A two-dimensional adaptive spectral element method. In: 13th AMA Computational Fluid Dynamics Conference , American Meteorological Society, Snowmass, CO .
Pedlosky , J., 1996 . Ocean Circulation Theory . Springer-Verlag , Heidelberg .
Rhines , P. B. and Young , W. R. 1982 . Homogenization of potential vorticity in planetary gyres . J. Fluid Mech . 122 , 347 – 367 .
Scott , R. B. and Straub , D. N. 1998 . Small viscosity behaviour of a homogeneous, quasi-geostrophic, ocean circulation model . J. Mar. Res . 56 , 1225 – 1258 .
Shchepetkin , A. E and O’Brien , J. 1996. A physically consistent formulation of lateral friction in shallow-water equation ocean models. Mon. Wea. Rev . 124 , 1285–130 0 .
Taylor , M. and Wingate , B. 2000 . A generalized diagonal mass matrix spectral element method for non-quadrilateral elements . Appl. Numer. Math . 33 , 259 – 265 .