h, p, k Least squares finite element processes for 1-D Helmholtz equation

International Journal for Computational Methods in Engineering Science and Mechanics

Volumn 7, Issue 4, 2006, Pages 263-291

  Surana, K S ^a   Gupta, P ^a   Tenpas, P W ^a   Reddy, J N ^b  

^a University of Kansas   (United States)

^b Texas AandM University   (United States)

Author keywords

Galerkin Method; Helmholtz Equation; Higher Order Spaces; Least Squares Method; Variational Consistency

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTATIONAL COMPLEXITY; GALERKIN METHODS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; NUMBER THEORY;

HELMHOLTZ EQUATION; HIGHER-ORDER SPACES; LEAST-SQUARES METHOD; VARIATIONAL CONSISTENCY;

FINITE ELEMENT METHOD;

EID: 33646254117     PISSN: 15502287     EISSN: 15502295     Source Type: Journal    
DOI: 10.1080/15502280500388284     Document Type: Article

References (22)

1. Goldstein. C. I., "The finite element method with non-uniform mesh sizes applied to the exterior Helmholtz problem," Numer. Math. 38. 61-82 (1981).
2. Aziz, A. K., Kellogg. R. B., and Stephens, A. B., "A two point boundary value problem with a rapidly oscillating Solution," Numer. Math. 53, 107-121 (1988).
3. Givoli Dan, and Joseph Keller. B., "A finite element method for large domains." Comput. Methods Appl. Mech. Engrg, 76, 41-66 (1989).
4. Harari, Isaac, and Hughes, Thomas J. R., "Finite element method for the Helmholtz equation in an exterior domain: Model problems," Comput. Methods Appl. Mech. Engrg. 87, 59-96 (1991).
5. Babuska, Ivo, Ihlenburg Frank, Paik, Ellen T., Sauter. Stefan A., "A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution." Comput. Methods Appl. Mech. Engrg. 128, 325-359 (1995).
6. Thompson Lonney. L., and Pinsky Peter M., "A Galerkin least-squares finite element method for the two-dimensional Helmholtz equation." Intentat, J. Numer. Methods Engrg. 38. 371-397 (1995).
7. Ihlenburg, F., and Babuska I., "Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of the FEM," Computers Math. Applic. 30, 9-37 (1995).
8. Babuska Ivo, M., and Sauter. Stefan A., "Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?," SIAM J. Numer. Anal. 34, 2392-2423 (1997).
9. Franca, Leopoldo, P., Farhat, Charbel, Macedo Antonini, P., and Lesoinne, Michel, "Residual-free bubbles for the Helmholtz equation," Internat. J. Numer. Methods Engrg. 40, 4003-4009 (1997).
10. Ihlenburg, F., and Babuska I., "Finite element solution of the Helmholtz equation with high wave number Part II: The h-p version of the FEM," SIAM J. Numer. Anal. 34. 315-358 (1997).
11. Franca Leopoldo, P., and Macedo Antonini P., "A two-level finite element method and its application to the Helmholtz equation." Intentat. J. Numer. Methods Engrg. 43, 23-32 (1998).
12. Deraemaeker Arnaud, Babuska Ivo, and Bouillard Philippe, "Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions," Internat, J. Numer. Methods Engrg. 46, 471-4-99 (1999).
13. Gelfand. I. M., and Fomin, S. V., Calculus of Variations., Dover. New York (2000).
14. Mikhlin. S. G., Variational Methods in Mathematical Physics., Pergamon Press, New York (1964).
15. Reddy, J. N., Functional Analysis and Variational Methods in Engineering. MeGraw-Hill, New York (1986).
16. Surana, K. S., Ahmadi, A. R., and Reddy, J. N., "k-version of finite element method for self-adjoint operators in BVR," Internat. J. Comp. Engng. Sci. 3(2). 155-218 (2002).
17. Surana. K. S., Ahmadi. A. R., and Reddy. J.N., "k-version of finite element method for non-self-adjoint operators in BVP," Internat. J. Comp. Engng. Sci. 4(4). 737-812 (2003).
18. Surana, K. S., Ahmadi, A. R., and Reddy, J. N., "k-version of finite element method for non-linear differential operators in BVP," Internal. J. Comp. Engng. Sci. 5(1), 133-207 (2004).
19. Surana, K. S., Rajwani. A., Reddy. J. N., and Nagar. A., "k-version of finite element method in singular boundary value problem" Linear Elastic Fracture Mechanics, IJCES (in review).
20. Surana, K. S., Petti, S. R., Ahmadi. A. R., and Reddy, J. N., "p-version of hierarchical interpolation functions for higher order continuity finite element models." Internat. J. Comp, Engng. Sci, 2(4), 357-382 (2001).
21. Surana. K. S., Gupta, P., Reddy J. N., and Tenpas, P. W. h, p, k least squares finite element processes for 2-D Helmholtz equation, IJNME (in review).
22. Surana, K. S., and Sandhu, J. S., "Investigation of diffusion in p-version LSFE and STLSFE formulations," Computational Mechanics 16, 151-169 (1995).