On the finite element solution of the pure Neumann problem

SIAM Review

Volumn 47, Issue 1, 2005, Pages 50-66

  Bochev, Pavel ^a   Lehoucq, R B ^a  

^a SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Finite elements; Neumann problem; Quadratic programming; Rayleigh Ritz minimization; Regularization

Indexed keywords

APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; LINEAR EQUATIONS; MATRIX ALGEBRA; OPTIMIZATION; PROBLEM SOLVING; QUADRATIC PROGRAMMING; THEOREM PROVING; VARIATIONAL TECHNIQUES;

ALGEBRAIC SOLUTION; FINITE ELEMENT SOLUTION; NEUMANN PROBLEM; RAYLEIGH-RITZ MINIMIZATION; REGULARIZATION; VARIATIONAL FRAMEWORK;

FINITE ELEMENT METHOD;

EID: 17444403192     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036144503426074     Document Type: Article

References (22)

1. O. Axelsson, Iterative Solution Methods , Cambridge University Press, Cambridge, UK, 1994.
2. E. Becker, G. Carey, and T. Oden, Finite Elements. An Introduction Vol. 1, Prentice-Hall, Englewood Cliffs, NJ, 1981.
3. D. Braess, Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics, Cambridge University Press, Cambridge, UK, 1997.
4. J. H. Bramle, J. E. Pasciak, and A. H. Schatz, The construction of preconditioners for elliptic problems by substructuring. I, Math. Comp., 47 (1986), pp. 103-134.
5. 2 projection Math. Comp., 56 (1991), pp. 463-476.
6. S. Brenner and R. Scott, The Mathematical Theory of Finite Element Methods, Springer-Verlag, New York, 1994.
7. F. Brezzi and M. Fortin Mixed and Hybrid Finite Element Methods, Springer-Verlag, Berlin, 1991.
8. G. Carey and T. Oden, Finite Elements. Computational Aspects, Vol. 3, Prentice-Hall, Englewood Cliffs, NJ, 1984.
9. R. Cook, D. Malkus, and M. Plesha, Concepts and Applications of Finite Element Analysis, 3rd ed., John Wiley and Sons, New York, 1989.
10. C. Farhat and M. Géradin, On the general solution by a direct method of a large-scale singular system of linear equations: Application to the analysis of floating structures, Internat. J. Numer. Methods Engrg., 41 (1998), pp. 675-696.
11. V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, Berlin, 1986.
12. P. Gresho and R. Sani, Incompressible Flow and the Finite Element Method, John Wiley and Sons, Chichester, UK, 1998.
13. T. Hughes, The Finite Element Method: Linear Static and Dynamic Analysis, Dover, New York, 2000.
14. C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge University Press, Cambridge, UK, 1987.
15. S. F. McCormik, Multilevel Adaptive Methods for Partial Differential Equations, SIAM, Philadelphia, 1989.
16. J. Nocedal and S. Wright, Numerical Optimization, Springer Verlag, New York, 1999.
17. M. Papadrakakis and Y. Fragakis, An integrated geometric-algebraic method for solving semi-definite problems in structural mechanics, Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 6513-6532.
18. A. Quarteroni and A. Valli Numerical Approximation of Partial Differential Equations, 2nd ed., Springer-Verlag, Berlin, 1997.
19. J. N. Reddy, An Introduction to the Finite Element Method, 2nd ed., McGraw-Hill, New York, 1993.
20. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method: Fluid Dynamics, Vol. 3, 5th ed., Butterworth-Heinemann, New York, 2000.
21. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method: Solid Mechanics, Vol. 2, 5th ed., Butterworth-Heinemann, New York, 2000.
22. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method: The Basis, Vol. 1, 5th ed., Butterworth-Heinemann, New York, 2000.