Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of the FEM

Computers & Mathematics with Applications - Tập 30 Số 9 - Trang 9-37 - 1995
Frank Ihlenburg1, Ivo Babuška1
1Institute for Physical Science and Technology, University of Maryland at College Park, College Park, MD 20742, U.S.A.

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Dautray, 1990, Vol. 1

Junger, 1986

Harari, 1991, Finite element method for the Helmholtz equation in an exterior domain: Model problems, Comp. Meth. Appl. Mech. Eng., 87, 59, 10.1016/0045-7825(91)90146-W

Bayliss, 1985, Turkel, On accuracy conditions for the numerical computation of waves, J. Comp. Phys., 59, 396, 10.1016/0021-9991(85)90119-6

Aziz, 1988, A two point boundary value problem with a rapidly oscillating solution, Numer. Math., 53, 107, 10.1007/BF01395880

Douglas, 1993, Frequency domain treatment of one-dimensional scalar waves, Mathematical Models and Methods in Applied Sciences, 3, 171, 10.1142/S0218202593000102

I. Babuška, F. Ihlenburg and Ch. Makridakis, Analysis and finite element methods for a fluid solid interaction problem in one dimension, Technical Note BN-1183, Institute for Physical Science and Technology, University of Maryland at College Park, (in preparation).

F. Ihlenburg and I. Babuška, Dispersion analysis and error estimation of Galerkin finite element methods for the Helmholtz equation, Int. J. Numer. Methods Eng. (to appear).

Babuška, 1994, A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution, 10.21236/ADA290280

Demkowicz, 1994, Asymptotic convergence in finite and boundary element methods: Part I: Theoretical results, Computers Math. Applic., 27, 69, 10.1016/0898-1221(94)90087-6

Harari, 1992, Galerkin/least squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains, Comp. Meth. Appl. Mech. Eng., 98, 411, 10.1016/0045-7825(92)90006-6

Thompson, 1995, A Galerkin least squares finite element method for the two-dimensional Helmholtz equation, Int. J. Numer. Methods Eng., 38, 371, 10.1002/nme.1620380303

Babuška, 1994, Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers

Achieser, 1953

John, 1982

Babuška, 1972, The mathematical foundations of the finite element method, 5

Strang, 1973

Samarskii, 1971

Ihlenburg, 1993, Finite element solution to the Helmholtz equation with high wavenumber—Part I: The h-version of the FEM

Babuška, 1994, Pollution error in the h-version of the FEM and the local quality of a-posteriori error estimators

Babuška, 1994, A-posteriori estimation and adaptive control of the pollution-error in the h-version of the FEM

Babuška, 1994, Pollution error in the h-version of the FEM and the local quality of recovered derivatives

Thompson, 1994, Complex wavenumber Fourier analysis of the p-version finite element method, Computational Mechanics, 13, 255, 10.1007/BF00350228

I. Babuška, I.N. Katz and B.S. Szabó, Finite element analysis in one dimension, In Lecture Notes, Springer-Verlag, (to appear).

Burnett, 1994, A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion, J. Acoust. Soc. Am., 96, 2798, 10.1121/1.411286

Harari, 1992, A cost comparison of boundary element and finite element methods for problems of time-harmonic acoustics, Comp. Meth. Appl. Mech. Eng., 97, 77, 10.1016/0045-7825(92)90108-V

Ihlenburg, 1994, Finite element solution to the Helmholtz equation with high wavenumber—Part II: The h-p-version of the FEM, SIAM J. Numer. Anal.

Schatz, 1974, An observation concerning Ritz-Galerkin methods with indefinite bilinear forms, Math. Comp., 28, 959, 10.1090/S0025-5718-1974-0373326-0

Szabó, 1991