Prismatic mixed finite elements for second order elliptic problems
Tóm tắt
In this paper, three families of mixed finite elements based on prisms are introduced. These spaces are analogues to those based on simplices and cubes in three space variables. Error estimates in L2 and H−5 are given.
Tài liệu tham khảo
F. Brezzi, J. Douglas Jr., R. Durán, M. Fortin,Mixed finite elements for second order elliptic problems in three variables, Numer. Math., 51 (1987), 237–250.
F. Brezzi, J. Douglas Jr., M. Fortin, L. D. Marini,Efficient rectangular mixed finite elements in two and three space variables, R.A.I.R.O. Modélisation Mathématique et Analyse Numérique, 21 (1987), 581–604.
F. Brezzi, J. Douglas Jr., L. D. Marini,Two families of mixed finite elements for second order elliptic problems, Numer. Math. 47 (1985), 217–235.
F. Brezzi, L. D. Marini, P. Pietra,Two-dimensional exponential fitting and applications to semiconductor device equations, SIAM J. Numer. Anal., to appear.
J. Douglas Jr., R. Durán, P. Pietra,Alternating-direction iteration for mixed finite element methods, Computing Methods in Applied Science and Engineering, VII, to appear.
J. Douglas, Jr., R. Durán, P. Pietra,Formulation of alternating-direction iterative methods for mixed methods in three space, in Numerical Approximation of Partial Differential Equations, 1987, E. L. Ortiz, ed., North-Holland, Amsterdam, 21–30.
J. Douglas Jr., P. Pietra,A description of some alternating-direction iterative techniques for mixed finite element methods, in Mathematical and Computational Methods in Seismic Exploration and Reservoir Modeling, 1986, W. E. Fitzgibbon, ed., SIAM, Philadelphia, 37–53.
J. Douglas Jr., J. E. Roberts,Global estimates for mixed methods for second order elliptic problems, Math. Comp., 45 (1985), 39–52.
J. C. Nedelec,A new family of mixed finite elements in R 3, Numer. Math., 50 (1986), 57–82.