Error estimates for least-squares mixed finite elements

A. I. Pehlivanov; G. F. Carey

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1994)

  • Volume: 28, Issue: 5, page 499-516
  • ISSN: 0764-583X

How to cite

top

Pehlivanov, A. I., and Carey, G. F.. "Error estimates for least-squares mixed finite elements." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 28.5 (1994): 499-516. <http://eudml.org/doc/193749>.

@article{Pehlivanov1994,
author = {Pehlivanov, A. I., Carey, G. F.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {error estimates; least-squares mixed finite element method; second-order elliptic problems; nonconforming},
language = {eng},
number = {5},
pages = {499-516},
publisher = {Dunod},
title = {Error estimates for least-squares mixed finite elements},
url = {http://eudml.org/doc/193749},
volume = {28},
year = {1994},
}

TY - JOUR
AU - Pehlivanov, A. I.
AU - Carey, G. F.
TI - Error estimates for least-squares mixed finite elements
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1994
PB - Dunod
VL - 28
IS - 5
SP - 499
EP - 516
LA - eng
KW - error estimates; least-squares mixed finite element method; second-order elliptic problems; nonconforming
UR - http://eudml.org/doc/193749
ER -

References

top
  1. [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. Zbl0338.90047MR365287
  2. [2] G. F CAREY, S. S. CHOW and M. R. SEAGER, 1985, Approximate Boundary-Flux Calculations, Comput. Methods Appl. Mech. Engrg., 50, 107-120. Zbl0546.73057MR802335
  3. [3] G. F. CAREY and J. T. ODEN, 1983, Finite Elements : A Second Course, vol. II, Prentice-Hall, Englewood Cliffs, N. J. Zbl0515.65075MR767804
  4. [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. Zbl0684.65083
  5. [5] C. L. CHANG, 1990, A least-squares finite element method for the Helmholtz equation, Comput. Methods Appl. Mech. Engrg., 83, 1-7. Zbl0726.65121MR1078694
  6. [6] T.-F. CHEN, 1986, On least-squares approximations to compressible flow problems, Numer. Methods Partial Differential Equations, 2, 207-228. Zbl0631.76082MR925373
  7. [7] P. G. CIARLET, 1978, The Finite Element Method for Elliptic Problems, North Holland, Amsterdam Zbl0383.65058MR520174
  8. [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. Zbl0261.65079MR375801
  9. [9] J. DOUGLAS and J. E. ROBERTS, 1985, Global estimates for mixed methods for second order elliptic equations, Math. Comp., 44, 39-52. Zbl0624.65109MR771029
  10. [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. Zbl0459.65072MR615890
  11. [11] P. GRISVARD, 1985, Elliptic Problems in Nonsmooth Domains. Pitman. Boston. Zbl0695.35060MR775683
  12. [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. Zbl0574.65123MR737949
  13. [13] M. KŘIŽEK and P. NEITTAANMAKI, 1984, On the validity of Friedrichs' inequalities, Math. Scand., 54, 17-26. Zbl0555.35003MR753060
  14. [14] L. M. MEHRA, 1978, Zur asymptotischen Verteilung der Eigenwerte des Maxwellschen Randwertproblems, Dissertation, Bonn. Zbl0411.35074MR544360
  15. [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. Zbl0469.65079MR588947
  16. [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. Zbl0463.65073MR627107
  17. [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. Zbl0451.65087MR605756
  18. [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. Zbl0806.65108MR1293520
  19. [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. Zbl0790.65079MR1248894
  20. [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. Zbl0362.65089MR483555
  21. [21] J. SARANEN, 1982, On an inequality of Friedrichs, Math. Scand., 51, 310-322. Zbl0524.35100MR690534
  22. [22] J. SARANEN, 1980, Über die Approximation der Lösungen der Maxwellschen Randwertaufgabe mit der Methode der finiten Elemente, Applicable Analysis, 10, 15-30. Zbl0454.65079MR572804

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.