Error estimates for least-squares mixed finite elements
Pehlivanov, A. I. ; Carey, G. F.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 28 (1994), p. 499-516 / Harvested from Numdam
Publié le : 1994-01-01
@article{M2AN_1994__28_5_499_0,
     author = {Pehlivanov, A. I. and Carey, G. F.},
     title = {Error estimates for least-squares mixed finite elements},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {28},
     year = {1994},
     pages = {499-516},
     mrnumber = {1295584},
     zbl = {0820.65065},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1994__28_5_499_0}
}
Pehlivanov, A. I.; Carey, G. F. Error estimates for least-squares mixed finite elements. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 28 (1994) pp. 499-516. http://gdmltest.u-ga.fr/item/M2AN_1994__28_5_499_0/

[1] F. Brezzi, 1974, On the existence, uniqueness and approximation of saddle point problems arising from Lagrange multipliers, RAIRO, Sér. Anal. Numér., 8, no. R-2, 129-151. | Numdam | MR 365287 | Zbl 0338.90047

[2] G. F Carey, S. S. Chow and M. R. Seager, 1985, Approximate Boundary-Flux Calculations, Comput. Methods Appl. Mech. Engrg., 50, 107-120. | MR 802335 | Zbl 0546.73057

[3] G. F. Carey and J. T. Oden, 1983, Finite Elements : A Second Course, vol. II, Prentice-Hall, Englewood Cliffs, N. J. | MR 767804 | Zbl 0515.65075

[4] G. F. Carey and Y. Shen, 1989, Convergence studies of least-squares finite elements for first order systems, Comm. Appl. Numer. Methods, 5, 427-434. | Zbl 0684.65083

[5] C. L. Chang, 1990, A least-squares finite element method for the Helmholtz equation, Comput. Methods Appl. Mech. Engrg., 83, 1-7. | MR 1078694 | Zbl 0726.65121

[6] T.-F. Chen, 1986, On least-squares approximations to compressible flow problems, Numer. Methods Partial Differential Equations, 2, 207-228. | MR 925373 | Zbl 0631.76082

[7] P. G. Ciarlet, 1978, The Finite Element Method for Elliptic Problems, North Holland, Amsterdam | MR 520174 | Zbl 0383.65058

[8] P. G. Ciarlet and P. A. Raviart, 1972, Interpolation theory over curved elements, with application to finite element methods, Comput. Methods Appl. Mech. Engrg., 1, 217-249. | MR 375801 | Zbl 0261.65079

[9] J. Douglas and J. E. Roberts, 1985, Global estimates for mixed methods for second order elliptic equations, Math. Comp., 44, 39-52. | MR 771029 | Zbl 0624.65109

[10] G. J. Fix, M. D. Gunzburger and R. A. Nicolaides, 1981, On mixed finite element methods for first order elliptic systems, Numer. Math., 37, 29-48. | MR 615890 | Zbl 0459.65072

[11] P. Grisvard, 1985, Elliptic Problems in Nonsmooth Domains. Pitman. Boston. | MR 775683 | Zbl 0695.35060

[12] J. Haslinger and P. Neittaanmäki, 1984, On different finite element methods for approximating the gradient of the solution to the Helmholtz equation, Comput. Methods Appl. Mech. Engrg., 42, 131-148. | MR 737949 | Zbl 0574.65123

[13] M. Křižek and P. Neittaanmaki, 1984, On the validity of Friedrichs' inequalities, Math. Scand., 54, 17-26. | MR 753060 | Zbl 0555.35003

[14] L. M. Mehra, 1978, Zur asymptotischen Verteilung der Eigenwerte des Maxwellschen Randwertproblems, Dissertation, Bonn. | MR 544360 | Zbl 0411.35074

[15] P. Neittaanmaki and R. Picard, 1980, Error estimates for the finite element approximation to a Maxwell-type boundary value problem, Numer Functional Analysis and Optimization, 2, 267-285. | MR 588947 | Zbl 0469.65079

[16] P Neittaanmaki and J. Saranen, 1981, On finite element approximation of the gradient for the solution of Poisson equation, Numer. Math., 37, 333-337. | MR 627107 | Zbl 0463.65073

[17] P. Neittaanmaki and J. Saranen, 1980, Finite element approximation of electromagnetic fields in three dimensional space, Numer. Functional Analysis and Optimization, 2, 487-506. | MR 605756 | Zbl 0451.65087

[18] A. I. Pehlivanov, G. F. Carey and R. D. Lazarov, 1993, Least-squares mixed finite elements for second order elliptic problems, SIAM J. Numer. Anal., to appear. | MR 1293520 | Zbl 0806.65108

[19] A. I. Pehlivanov, G. F Carey, R. D. Lazarov and Y. Shen, 1993, Convergence analysis of least-squares mixed finite elements, Computing, 51, 111-123. | MR 1248894 | Zbl 0790.65079

[20] P. A. Raviart and J. M. Thomas, 1977, A mixed finite element method for 2nd order elliptic problems, Lect Notes in Math., Springer-Verlag, v. 606, 292-315. | MR 483555 | Zbl 0362.65089

[21] J. Saranen, 1982, On an inequality of Friedrichs, Math. Scand., 51, 310-322. | MR 690534 | Zbl 0524.35100

[22] J. Saranen, 1980, Über die Approximation der Lösungen der Maxwellschen Randwertaufgabe mit der Methode der finiten Elemente, Applicable Analysis, 10, 15-30. | MR 572804 | Zbl 0454.65079