Two families of mixed finite elements for second order elliptic problems
Tóm tắt
Two families of mixed finite elements, one based on triangles and the other on rectangles, are introduced as alternatives to the usual Raviart-Thomas-Nedelec spaces. Error estimates inL
2
(Ω) andH
−5
(Ω) are derived for these elements. A hybrid version of the mixed method is also considered, and some superconvergence phenomena are discussed.
Tài liệu tham khảo
Arnold, D.N. Brezzi, F.: Mixed and nonconforming finite element methods: Implementation, postprocessing, and error estimates. RAIRO. (To appear)
Brezzi, F.: On the existence, uniqueness, and approximation of saddle point problems arising from Lagrangian multipliers. RAIRO, Anal. numér.2, 129–151 (1974)
Brezzi, F., Douglas, Jr., J., Marini, L.D.: Variable degree mixed methods for second order elliptic problems. (To appear)
Brezzi, F., Douglas, Jr., J., Marini, L.D.: Recent results on mixed methods for second order elliptic problems. (To appear)
Douglas, Jr., J., Roberts, J.E.: Mixed finite element methods for second order elliptic problems. Mathemática Applicada e Computacional1, 91–103 (1982)
Douglas, Jr., J., Roberts, J.E.: Global estimates for mixed methods for second order elliptic equations. Math. Comput.44, 39–52 (1985)
Dupont, T., Scott, R.: Polynomial approximation of functions in Sobolev space, Math. Comput.34, 441–463 (1980)
Fraeijs de Veubeke, B.X.: Displacement and equilibrium models in the finite element method. Stress analysis, O.C. Zienkiewicz, G. Holister, eds. New York: Wiley 1965
Fraeijs de Veubeke, B.X.: Stress function approach, World Congress on the Finite Element Method in Structural Mechanics. Bournemouth, 1975
Handbook of mathematical functions, M. Abromowitz, I. Stegun, eds., Chapter 22 (O.W. Hochstrasser)
Johnson, C. Thomée, V.: Error estimates for some mixed finite element methods for parabolic type problems. RAIRO, Anal. numér.15, 41–78 (1981)
Nedelec, J.C.: Mixed finite elements in ℝ3. Numer. Math.35, 315–341 (1980)
Nitsche, J.: Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg36, 9–15 (1970/1971)
Raviart, P.A., Thomas, J.M.: A mixed finite element method for 2nd order elliptic problems. Mathematical aspects of the finite element method. Lecture Notes in Mathematics, Vol. 606. Berlin-Heidelberg-New York: Springer 1977