Error estimates for the finite element solution of variational inequalities. Part II. Mixed methods. (English) Zbl 0427.65077


65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
49J40 Variational inequalities


Zbl 0369.65030
Full Text: DOI EuDML


[1] Adams, R.A.: Sobolev spaces. New York: Academic Press 1975 · Zbl 0314.46030
[2] Babuska, I., Oden, J.T., Lee, J.K.: Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems. The Texas Institute for Computational Mechanics, University of Texas at Austin, 1975
[3] Brézis, H., Kinderlehrer, D.: The smoothness of solutions to nonlinear variational inequalities, Indiana Univ. Math. L.23, 831-844 (1974) · Zbl 0278.49011
[4] Brézis, H.: Nouveaux théorèmes de régularité pour les problèmes unilatéraux. Rencontre entre physiciens théoriciens et mathématiciens, Strasbourg12 (1971)
[5] Brézis, H.: Seuil de régularité pour certains problèmes unilatéraux. C. R. Acad. Sci. Paris273, 35-37 (1971) · Zbl 0214.10703
[6] Brézis, H., Stampacchia, G.: Sur la régularité de la solution d’inéquations elliptiques. Bull. Soc. Math. France96, 153-180 (1968) · Zbl 0165.45601
[7] Brezzi, F.: On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. R.A.I.R.O.2, 129-151 (1974) · Zbl 0338.90047
[8] Brezzi, F., Raviart, P.A.: Mixed finite element methods for fourth order elliptic equations. In: Topics in numerical analysis, Vol. III (J.J.H. Miller, ed.). London: Academic Press 1977 · Zbl 0434.65085
[9] Brezzi, F., Hager, W.W., Raviart, P.A.: Error estimates for the finite element solution of variational inequalities. Part I. Primal theory. Numer. Math.28, 431-443 (1977) · Zbl 0369.65030
[10] Frehse, J.: Two dimensional variational problems with thin obstacles. Math. Z.143, 279-288 (1975) · Zbl 0302.49002
[11] Gagliardo, E.: Proprietà di alcuni classi di funzioni in pui variablili. Ricerche Mat7, 102-137 (1958) · Zbl 0089.09401
[12] Giaquinta, M., Modica, G.: Regolarità lipschitziana per le soluzioni di alcuni problemi di minimo con vincolo. Ann. Mat. Pura Appl. (to appear) · Zbl 0325.49009
[13] Hlavá?ek, I.: Dual finite element analysis for elliptic problems with obstacles on the boundary. I. To appear
[14] Hlavá?ek, I.: Dual finite element analysis for unilateral boundary value problems. Apl. Mat.22, 14-51 (1977)
[15] Johnson, C.: On the convergence of a mixed finite element method for plate bending problems. Numer. Math.21, 43-62 (1973) · Zbl 0264.65070
[16] Lions, J.L.: Problémes aux limites dans les équations aux dérivées partielles. Montreal, Canada: University of Montreal Press 1965 · Zbl 0143.14003
[17] Lions, J.L.: Equations aux dérivées partielles et calcul des variations. Cours de la Faculté des Sciences de Paris, 1967
[18] Oden, J.T., Reddy, J.N.: On mixed finite element approximations. Texas Institute for Computational Mechanics, University of Texas at Austin, 1974
[19] Raviart, P.A., Thomas, J.M.: A mixed finite element method for second order elliptic problems. In: Mathematical aspects of finite element methods. Lecture notes in mathematics. Vol. 606, pp. 292-315. Berlin-Heidelberg-New York: Springer 1977
[20] Stampacchia, G., Kinderlehrer, D.: Book to appear
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