×

Error estimates for mixed methods. (English) Zbl 0467.65062


MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
35J25 Boundary value problems for second-order elliptic equations
31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
PDFBibTeX XMLCite
Full Text: EuDML

References:

[1] 1 I. BABU KA, Error-Bounds for Finite Element Method, Numer Math , Vol. 16, 1971, pp. 322-333. Zbl0214.42001 MR288971 · Zbl 0214.42001
[2] 2 I. BABU KA and A. Aziz, Survey Lectures on the Mathematical Foundations of the Finite Element Method in The Mathematical Foundations of the Finite Element Method with Application to Partial Differential Equations, A. K. Aziz, Ed, Academic Press, New York, 1973, pp. 5-359. Zbl0268.65052 · Zbl 0268.65052
[3] 3 I. BABU KA, J. OSBORN and J. PITKARANTA, Analysis of Mixed Methods for 4th Order Elliptic Equations (to appear). Zbl0816.76060 · Zbl 0816.76060
[4] 4 J. BRAMBLE and S. HILBERT, Estimation of Linear Functionals on Sobolov Spaces with Application to Fourier Transforms and Spline Interpolation, S.I. A. M . J. Numer Anal, Vol .13, 1976, pp. 185-197. Zbl0201.07803 · Zbl 0201.07803
[5] 5 F. BREZZI, On theExistence, Uniqueness and Approximation of Saddle-Point Problems Ansing from Lagrangian Multipliers, R. A. I. R. O. , Vol. 8 R2, 1974, pp 129-151. Zbl0338.90047 MR365287 · Zbl 0338.90047
[6] 6 F. BREZZI, Sur la méthode des éléments finis hybrides pour le problème biharmonique, Numer. Math., Vol. 24, 1975, pp 103-131. Zbl0316.65029 MR391538 · Zbl 0316.65029
[7] 7 F. BREZZI and P. RAVIART, Mixed Finite Element Methods for 4th Ordej Elliptic Equations, Topics inNumencal Analysis III, J. MILLER, Ed , Academic Press, 1978. Zbl0434.65085 · Zbl 0434.65085
[8] 8 P. GIARLET, The Finite Element Method for Elliptic Problems, North-Holland, 1978. Zbl0383.65058 MR520174 · Zbl 0383.65058
[9] .9 P. CIARLET and P. RAVIART, A Mixed Finite Element Method for the Biharmonic Equation, Symposium on Mathematical Aspects of Finite Elements in Partial Differential Equations, C. DE BOOR, Ed., Academic Press, New York, 1974, pp. 125-143. Zbl0337.65058 MR657977 · Zbl 0337.65058
[10] 10 M. CROUZEIX and P. RAVIART, Conforming and Nonconforming Finite Element Methods for Solving the Stationary Stokes Equations I, R. A. I. R. O. , Vol. R-3, 1973, pp 33-76. Zbl0302.65087 MR343661 · Zbl 0302.65087
[11] 11 M. FORTIN, Analysis of the Convergence of Mixed Finite Element Methods, R.A.I.R.O.,Vol. 11, 1977, pp. 341-354. Zbl0373.65055 MR464543 · Zbl 0373.65055
[12] 12 R. GLOWINSKI, Approximations externes, par elements finis deLagrange d’ordre un et deux, du probleme de Dinchlet pour l’operateur biharmonique Methodes iteratives de resolution des problemes approches In Topics in Numencal Analysis, J.J. .H MILLER, Ed., Academic Press, New York, 1973, pp. 123-171. Zbl0277.35003 MR351120 · Zbl 0277.35003
[13] 13 P. GRISVARD, Singular Solutions of Elliptic Boundary Value Problems, Lecture Notes,University of Maryland (to appear). · Zbl 0567.35025
[14] 14 L. HERRMANN, Finite Element Bending Analysis for Plates, J. Eng Mech Div A. S.C. E. E. M5, Vol. 93, 1967, pp. 49-83.
[15] 15 L. HERRMANN, A Bending Analysis for Plates, Proc. Conf. On Matrix Methods in Structural Mechanics, AFFDL-TR-66-68, pp. 577-604.
[16] 16 C. JOHNSON, On the Convergence of a Mixed Finite Element Method for Plate Bending Problems, Numer Math , Vol. 21, 1973, pp. 43-62. Zbl0264.65070 MR388807 · Zbl 0264.65070
[17] 17 R. KELLOGG and J. OSBORN, A regularity Result for the Stokes Problem, J Funct Anal., Vol. 21, 1976, pp. 397-431. Zbl0317.35037 MR404849 · Zbl 0317.35037
[18] 18 B. MERCIER, Numerical Solution of the Biharmonic Problem by Mixed Finite Elements of Class C , Bull. Un. Mat. Ital. , Vol. 10, 1974, pp. 133-149. Zbl0332.65058 MR378442 · Zbl 0332.65058
[19] 19 T. MIYOSHI, Finite Element Method for the Solution of Fourth Order Partial Differential Equations, Kunamoto J. Sc. (Math.), Vol. 9, 1973, pp. 87-116. Zbl0249.35007 MR386298 · Zbl 0249.35007
[20] 20 J. ODEN, Some Contributions to the Mathematical Theory of Mixed Finite Element Approximations In Theory and Practice in Finite Element Structural Analysis, University of Tokyo Press, 1973, pp. 3-23. Zbl0374.65060 · Zbl 0374.65060
[21] 21 R. RANNACHER, On Nonconforming and Mixed Finite Element Methods for Plate Bending Problems The Linear Case, R. A. I. R. O. , Vol. 13, 1979, pp. 369-387. Zbl0425.35042 MR555385 · Zbl 0425.35042
[22] 22 P. RAVIART and J. THOMAS, A Mixed Finite Element Method for 2nd Order Elliptic Problems, Lecture Notes in math , No 606, Berlin-Heidelberg-New York, Springer, 1977, pp. 292-315. Zbl0362.65089 MR483555 · Zbl 0362.65089
[23] 23 R. SCHOLZ, Approximation von Sattelpunkten mit finiten Elementen, Tagungsband, Bonn. Math. Schr., Vol.. 89, 1976, pp. 53-66. Zbl0359.65096 MR471377 · Zbl 0359.65096
[24] 24 R. SCHOLZ, A Mixed Method for 4th Order Problems using Linear Finite Elements, R. A. I. R. O. , Vol. 12, 1978, pp. 85-90. Zbl0382.65059 MR483557 · Zbl 0382.65059
[25] 25 J. THOMAS, Sur l’Analyse numérique des méthodes d’élements finis hybrides et mixtes, Thesis, Pierre-et-Marie-Curie, Paris, 1977.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.