On the combined effect of boundary approximation and numerical integration on mixed finite element solution of 4th order elliptic problems with variable coefficients
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 33 (1999) no. 4, pp. 807-836.
@article{M2AN_1999__33_4_807_0,
     author = {Bhattacharyya, Pulin K. and Nataraj, Neela},
     title = {On the combined effect of boundary approximation and numerical integration on mixed finite element solution of 4th order elliptic problems with variable coefficients},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     pages = {807--836},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {4},
     year = {1999},
     zbl = {0942.65133},
     mrnumber = {1726487},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1999__33_4_807_0/}
}
TY  - JOUR
AU  - Bhattacharyya, Pulin K.
AU  - Nataraj, Neela
TI  - On the combined effect of boundary approximation and numerical integration on mixed finite element solution of 4th order elliptic problems with variable coefficients
JO  - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY  - 1999
DA  - 1999///
SP  - 807
EP  - 836
VL  - 33
IS  - 4
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/M2AN_1999__33_4_807_0/
UR  - https://zbmath.org/?q=an%3A0942.65133
UR  - https://www.ams.org/mathscinet-getitem?mr=1726487
LA  - en
ID  - M2AN_1999__33_4_807_0
ER  - 
%0 Journal Article
%A Bhattacharyya, Pulin K.
%A Nataraj, Neela
%T On the combined effect of boundary approximation and numerical integration on mixed finite element solution of 4th order elliptic problems with variable coefficients
%J ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
%D 1999
%P 807-836
%V 33
%N 4
%I EDP-Sciences
%G en
%F M2AN_1999__33_4_807_0
Bhattacharyya, Pulin K.; Nataraj, Neela. On the combined effect of boundary approximation and numerical integration on mixed finite element solution of 4th order elliptic problems with variable coefficients. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 33 (1999) no. 4, pp. 807-836. http://www.numdam.org/item/M2AN_1999__33_4_807_0/

[1] R.A. Adams, Sobolev Spaces. Academic Press, NewYork (1975). | MR | Zbl

[2] I. Babuska, Error Bounds for Finite Element Method. Numer. Math. 16 (1971) 322-333. | EuDML | MR | Zbl

[3] I. Babuska and J.E. Osborn, Eigenvalue Problems, in Handbook of Numerical Analysis, Vol. 2, Part 1, J.L. Lions and P.G. Ciarlet Eds., North-Holland, Amsterdam (1991) 641-787. | MR | Zbl

[4] S. Balasundaram and P.K. Bhattacharyya, On Existence of Solution of the Dirichlet Problem of Fourth Order Partial Differential Equations with Variable Coefficients. Quart. Appl. Math. 39 (1983) 311-317. | MR | Zbl

[5] S. Balasundaram and P.K. Bhattacharyya, A Mixed Finite Element Method for Fourth Order Elliptic Equations with Variable Coefficients. Comput. Math. Appl 10 (1984) 245-256. | MR | Zbl

[6] S. Balasundaram and P.K. Bhattacharyya, A Mixed Finite Element Method for Fourth Order Elliptic Operators with Variable Coefficients, 4th Int. Symp. on Finite Element Methods in Flow Problems, Chuo University, Tokyo (1982), in Finite Element Analysis of Flow Problems, T. Kawai Ed., Tokyo University Press (1982) 995-1001. | Zbl

[7] S. Balasundaram and P.K. Bhattacharyya, Mixed Finite Element Method for Fourth Order Partial Differential Equations. ZAMM 66 (1986) 489-499. | MR | Zbl

[8] M. Bernadou, Méthodes d'éléments finis pour les problèmes de coques minces. Collection Recherches en Mathématiques Appliquées, Masson, Paris (1994).

[9] P.K. Bhattacharyya and N. Nataraj, Error Estimates for Isoparametric Mixed Finite Element Solution of 4th Order Elliptic Problems with Variable Coefficients (submitted). | Zbl

[10] P.K. Bhattacharyya, Mixed Finite Element Method for Fourth Order Elliptic Operators with Variable Coefficients, In Proc. of 6th Joint France-Italy- USSR Symp. on Numerical Solution of Nonlinear Problems, INRIA, France (1983) 127-144; Russian Translation, in Methods of Computational Mathematics and Mathematical Modelling, Computational Mathematics Section, Academy of Sciences, Moscow, USSR (1985) 76-99. | MR | Zbl

[11] P.K. Bhattacharyya, S. Gopalsamy and S. Balasundaram, On a Mixed Finite Element Method for Clamped Anisotropic Plate Bending Problems. Internat. J. Numer. Methods Engrg. 28 (1989) 1351-1370. | Zbl

[12] P.K. Bhattacharyya and S. Balasundaram, A Mixed Finite Element Method for Fourth Order Elliptic Problems with Variable Coefficients. J. Comput. Appl. Math. 22 (1988) 1-24. | MR | Zbl

[13] F. Brezzi, On the Existence, Uniqueness and Approximation of Saddle-Point Problems Arising from Lagrangian Multipliers. RAIRO Anal. Numér. 8 (1974) 129-151. | Numdam | MR | Zbl

[14] F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag (1991). | MR | Zbl

[15] F. Brezzi and P.A. Raviart, Mixed Finite Element Methods for 4th Order Elliptic Equations, in Topics in Nufnerical Analysis III, J. Miller Ed., Academic Press, New York (1978) 33-56. | MR | Zbl

[16] P.G. Ciarlet, Basic Error Estimates for Elliptic Problems, in Handbook of Numerical Analysis, Vol. 2, Part 1, J.L. Lions and P.G. Ciarlet Eds., North-Holland, Amsterdam (1991). | MR | Zbl

[17] P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978). | MR | Zbl

[18] P.G. Ciarlet and P.A. Raviart, A Mixed Finite Element Method for the Biharmonic Equation, in Symp. on Mathematical Aspects of Finite Elements in Partial Differential Equations, C. de Boor Ed., Academic Press, New York (1974) 125-145. | MR | Zbl

[19] P.G. Ciarlet and P.A Raviart, The Combined Effect of Curved Boundaries and Numerical Integration in Isoparametric Finite Element Methods, in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A.K. Aziz Ed., Academic Press, New York (1972) 409-474. | MR | Zbl

[20] S. Gopalsamy and P.K. Bhattacharyya, On Existence and Uniqueness of Solution of Boundary Value Problems of Fourth Order Elliptic Partial Differential Equations with Variable Coefficients. J. Math. Anal. Appl. 136 (1988) 589-608. | MR | Zbl

[21] P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston (1985). | MR | Zbl

[22] K. Hellan, Analysis of Elastic Plates in Flexure by a Simplified Finite Element Method. Acta Polytech. Scand., Civil Engineering Series, Trondheim, 46 (1967). | Zbl

[23] L. Herrmann, Finite Element Bending Analysis for Plates. J. Eng. Mech. Div. ASCE 93, EM 5 (1967) 49-83.

[24] V.A. Kondratev, Boundary Value Problems for Elliptic Equations in Domains with Conical or Angular Points. Trudy Moskov. Mat. Obshch. 16 (1967) 7209-292. | MR | Zbl

[25] S.G. Leknitskii, Anisotropic Plates. Gordon and Breach Science Publishers, New York (1968).

[26] J.L. Lions, Problèmes aux Limites dans les Équations aux Dérivées Partielles. Les Presses de l'Université de Montréal, Montréal (1965). | MR | Zbl

[27] L. Mansfield, Approximation of the Boundary in the Finite Element solution of fourth order problems. SIAM J. Numer. Anal. 15 (1978) 568-579. | MR | Zbl

[28] T. Miyoshi, A finite element method for the solution of fourth order partial differential equations. Kumamoto J. Sci. (Math.) 9 (1973) 87-116. | MR | Zbl

[29] N. Nataraj, P.K. Bhattacharyya, S. Balasundaram and S. Gopalsamy, On a Mixed-Hybrid Finite Element Method for Anisotropic Plate Bending Problems. Internat. J. Numer. Methods Engrg. 39 (1996) 4063-4089. | MR | Zbl

[30] J.T. Oden and G.F Carey, Finite Elements-Mathematical Aspects IV, The Texas Finite Element Series. Prentice Hall, Eaglewood Cliffs, New Jersey (1983). | MR | Zbl

[31] A.B. Ouaritini, Méthodes d'éléments finis mixtes pour des problèmes de coques minces. Ph.D. thesis, University of Pau et Pays de L'Adour, France (1984).

[32] P.A. Raviart and J.M. Thomas, Introduction à l'Analyse Numérique des Équations aux Dérivées Partielles. Mason, Paris (1983). | Zbl

[33] J.E Roberts and J.M. Thomas, Mixed and Hybrid Methods, in Handbook of Numerical Analysis, Vol. 2, Part 1, J.L Lions and P.G. Ciarlet Eds., North-Holland, Amsterdam (1991) 523-633. | MR | Zbl

[34] R. Scholtz, A Mixed Method for 4th order Problems Using Linear Finite Elements. RAIRO Anal Numér. 12 (1978) 85-90. | Numdam | MR | Zbl

[35] R. Scott, Finite Element Techniques for Curved Boundaries. Ph.D. thesis, M.I.T. (1973).

[36] G. Strang and G.J. Fix, An Analysis of the Finite Element Method. Prentice-Hall, New York (1973). | MR | Zbl

[37] S. Timoshenko and S. Woinowsky-Kreiger, Theory of Plates and Shells. McGraw-Hill Book Company, New York (1959). | JFM

[38] A. Zeníšek, Nonlinear Elliptic and Evolution Problems and their Finite Element Approximations. Academic Press, New York (1990). | MR | Zbl

[39] M. Zlamal, Curved elements in the finite element method, I. SIAM J. Numer. Anal. 10 (1973) 229-240. | MR | Zbl

[40] M. Zlamal, Curved elements in the finite element method, II. SIAM J. Numer. Anal. 11 (1974) 347-362. | MR | Zbl