Error analysis in L p ⩽p⩽∞, for mixed finite element methods for linear and quasi-linear elliptic problems
ESAIM: Modélisation mathématique et analyse numérique, Tome 22 (1988) no. 3, pp. 371-387. 
@article{M2AN_1988__22_3_371_0,
     author = {Dur\'an, Ricardo G.},
     title = {Error analysis in $L^p \leqslant p \leqslant \infty $, for mixed finite element methods for linear and quasi-linear elliptic problems},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {371--387},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {22},
     number = {3},
     year = {1988},
     mrnumber = {958875},
     zbl = {0698.65060},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1988__22_3_371_0/}
}
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Durán, Ricardo G. Error analysis in $L^p \leqslant p \leqslant \infty $, for mixed finite element methods for linear and quasi-linear elliptic problems. ESAIM: Modélisation mathématique et analyse numérique, Tome 22 (1988) no. 3, pp. 371-387. http://www.numdam.org/item/M2AN_1988__22_3_371_0/

[1] F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, R.A.I.R.O., Anal. Numér. 2, 1974, pp. 129-151. | Numdam | MR | Zbl

[2] F. Brezzi, J. Douglas Jr., L.D. Marini , TWOfamilies of mixed finite elements for second order elliptic problems, Numer. Math. 47, 1985, pp. 217-235. | MR | Zbl

[3] A.P. Calderon, A. Zygmund, On the existence of certain singular integrals, Acta Math. 88, 1952, pp. 85-139. | MR | Zbl

[4] S. Campanato, G. Stampacchia, Sulle maggiorazioni in L p nella teoria della equazioni ellittiche, Boll. UMI 20, 1965, pp. 393-399. | MR | Zbl

[5] J. Douglas Jr., R. Ewing, M. Wheeler, Approximation of the pressure by a mixed method in the simulation of miscible displacement, R.A.I.R.O., Anal. Numér. 17, 1983, pp. 17-33. | Numdam | MR | Zbl

[6] J. Douglas Jr., I. Martinez Gamba, C. Squeff, Simulation of the transient behavior of one dimensional semiconductor device, to appear. | Zbl

[7] J. Douglas Jr., J.E. Roberts, Mixed finite element methods for second order elliptic problems. Mat. Aplic. Comp. 1, 1982, pp. 91-103. | MR | Zbl

[8] J. Douglas Jr., J.E. Roberts, Global estimates for mixed methods for second order elliptic equations, Math. Comp. 44, 1985, pp. 39-52. | MR | Zbl

[9] M. Fortin, An analysis of the convergence of mixed finite element methods, R.A.I.R.O., Anal. Numer. 11, 1977, pp. 341-354. | Numdam | MR | Zbl

[10] L. Gastaldi, R. H. Nochetto, Optimal L ∞ -error estimates for nonconforming and mixed finite element methods of lowest order. Numer. Math. 50, 3, 1987, pp. 587-611. | MR | Zbl

[11] L. Gastaldi, R. H. Nochetto, On L ∞ -accuracy of mixed finite element methods for second order elliptic problems, to appear. | Zbl

[12] L. Gastaldi, R. H. Nochetto, Sharp maximum norm error estimates for general mixed finite element approximations to second order elliptic equations, to appear. | Numdam | MR | Zbl

[13] D. Gilbarg, N.S Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin, 1983. | MR | Zbl

[14] C. Johnson, V. Thomee, Error estimates for some mixed finite element methods for parabolic type problems, R.A.I.R.O., Anal. Numer. 15, 1981, pp. 41-78. | Numdam | MR | Zbl

[15] Y. Kwon, F. Milner, Some new L ∞ estimates for mixed finite element methods, to appear. | Zbl

[16] Y. Kwon, F. Milner, L ∞ -error estimates for mixed methods for semilinear second order elliptic problems, to appear. | Zbl

[17] F. Milner, Mixed finite element methods for quasilinear second-order elliptic problems, Math. Comp. 44, 1985, pp. 303-320. | MR | Zbl

[18] J. Nedelec, Mixed finite elements in R 3 , Numer. Math. 35, 1980, pp. 315-341. | MR | Zbl

[19] J. A. Nitsche, L ∞ -convergence of finite element methods, 2nd Conference on Finite Elements, Rennes, France, May 12-14 (1975). | MR

[20] R. Rannacher, R. Scott, Some optimal error estimates for piecewise linear finite element approximations, Math. Comp. 38, 1982, pp. 437-445. | MR | Zbl

[21] P. A. Raviart, J. M. Thomas, A mixed finite element method for second order elliptic problems, Mathematical Aspects of the Finite Element Method, Lecture Notes in Math N 606, Springer-Verlag, Berlin, 1977, pp. 292-315. | MR | Zbl

[22] M. Schechter, On L p estimates and regularity, I., Amer. J. Math. 85, 1963, pp. 1-13. | MR | Zbl

[23] R. Scholz, L ∞ -convergence of saddle-point approximations for second order problems, R.A.I.R.O., Anal. Numer. 11, 1977, pp. 209-216. | Numdam | MR | Zbl

[24] R. Scholz, Optimal L ∞ -estimates for a mixed finite element for elliptic and parabolic problems, Calcolo 20, 1983, pp. 355-377. | MR | Zbl

[25] R. Scholz, A remark on the rate of convergence for mixed finite element method for second order problems, Numer. Funct. Anal. Optim. 4, 1981-1982, pp. 269-277. | MR | Zbl

[26] E. Stein, Singular integrals and differantiability propreties of functions, Princeton University Press, Princeton (1970). | Zbl