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A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution. (English) Zbl 0863.73055
Summary: When using the Galerkin FEM for solving the Helmholtz equation in two dimensions, the error of the corresponding solution differs substantially from the error of the best approximation, and this effect increases with higher wave number $k$. In this paper, we will design a generalized finite element method for the Helmholtz equation such that the pollution effect is minimal.

MSC:
74S05Finite element methods in solid mechanics
74J20Wave scattering (solid mechanics)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
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References:
[1] Babuška, I.; Osborn, J. E.: Generalized finite element methods: their performance and their relation to mixed methods. SIAM J. Numer. anal. 20, No. 3, 510-536 (1983) · Zbl 0528.65046
[2] Babuška, I. M.; Sauter, S. A.: Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers. Technical report BN-1172 (1994) · Zbl 0894.65050
[3] Hackbusch, W.: Elliptic differential equations. (1992) · Zbl 0755.35021
[4] Harari, I.; Hughes, T. J. R.: Finite element methods for the Helmholtz equation in an exterior domain: model problems. Comput. methods appl. Mech. engrg. 87, 59-96 (1991) · Zbl 0760.76047
[5] Ihlenburg, F.; Babuška, I.: Finite element solution to the Helmholtz equation with high wave number. Part I: The h-version of the FEM. Comput. math. Appl. 30, No. 9, 9-37 (1995) · Zbl 0838.65108
[6] F. Ihlenburg and I. Babuška, Dispersion analysis and error estimation of Galerkin finite element methods for the numerical computation of waves, Int. J. Numer. Methods Engrg., in press.
[7] F. Ihlenburg and I. Babuška, Finite element solution to the Helmholtz equation with high wave number. Part II: The h-p version of the FEM, SIAM J. Numer. Anal., to appear. · Zbl 0884.65104
[8] Keller, J. B.; Givoli, D.: Exact non-reflecting boundary conditions. J. comp. Phys. 82, 172-192 (1989) · Zbl 0671.65094
[9] Thompson, L. L.; Pinsky, P. M.: A Galerkin least squares finite element method for the two-dimensional Helmholtz equation. Int. J. Numer. methods engrg. 38, 371-397 (1995) · Zbl 0844.76060