Abstract
This non-conforming extension of the finite element method is illustrated with a model elliptic problem and other applications are sketched. New results concerning domain decomposition and the construction of a solenoidal basis for the Stokes equations are described.
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Babuška, I., Suri, M.: The p and h - p versions of the finite element method, an overview. Comput. Methods Appl. Mech. Engrg. 80, (1990), no. 1–3, 5–26.
Bernardi, C., Maday, Y., Patera, A. T.: Domain decomposition by the mortar element method, Asymptotic and numerical methods for partial differential equations with critical parameters (Beaune, 1992 ) 269–286, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 384, Kluwer Acad. Publ., Dordrecht, 1993.
Cayco, M., Foster, L., Swann, H.: On the convergence rate of the cell discretization algorithm for solving elliptic problems, Math. Comp, 64, 1397–1419 (1995).
Dorr, M. R.: On the discretization of interdomain coupling in elliptic boundary-value problems. In T.F. Chan, R. Glowinski, J. Periaux and O. B. Widlund, editors. Domain Decomposition Methods, SIAM, 1989.
Greenstadt, J.: Cell discretization, in Conference on Applications of Numerical Analysis, J.H. Morris, ed., Lecture Notes in Mathematics, 228, Springer-Verlag, New York, 1971, 70–82.
Greenstadt, J.: The cell discretization algorithm for elliptic partial differential equations, SIAM J. Sci. Stat. Comput. Vol 3, no. 3, (1982), 261–288.
Hui, G., Swann, H.: On orthogonal polynomial bases for triangles and tetrahedra invariant under the symmetric group, Contemp. Math. vol. 218, (1998) 438–446.
Raviart, P. A., Thomas, J. M.: Primal hybrid finite element methods for second order elliptic equations, Math. Comp., vol. 31 no. 138, (1977), 391–413.
Rice, J. R., Vavalis, E. A., Yang, D.: Analysis of a nonoverlapping domain decomposition method for elliptic partial differential equations, J. Comp. Appl. Math. 87, (1997), 11–19.
Swann, H.: On the use of Lagrange multipliers in domain decomposition for solving elliptic problems, Math. Comp. 60, No. 201, Jan, 1993, 49–78.
Swann, H.: Error estimates using the cell discretization method for some parabolic problems, J. Comp. Appl. Math. 66, (1996) 497–514
Swann, H.: Error estimates using the cell discretization method for second-order hyperbolic equations, Numer. Methods Partial Differential Eq. 13, (1997), 531–548.
Swann, H.: Error estimates using the cell discretization method for steady-state convection-diffusion equations, J. Comput. Appl. Math, 82, (1997), 389–405.
Swann, H.: On approximating the solution of the stationary Stokes equations using the cell discretization algorithm, submitted, Numer. Methods Partial Differential Eq., 1998.
Swann, H.: On using the cell discretization algorithm for mixed boundary value problems and domain decomposition, to appear, J. Comput. Appl. Math., Fall, 1999.
Swann, H.: On approximating the solution of the non-stationary Stokes equations using the cell discretization algorithm, preliminary report, 1998, San Jose State Univ.
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Swann, H. (2000). The Cell Discretization Algorithm; An Overiew. In: Cockburn, B., Karniadakis, G.E., Shu, CW. (eds) Discontinuous Galerkin Methods. Lecture Notes in Computational Science and Engineering, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59721-3_44
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DOI: https://doi.org/10.1007/978-3-642-59721-3_44
Publisher Name: Springer, Berlin, Heidelberg
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