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A least-squares method for the Helmholtz equation. (English) Zbl 0943.65127

A least squares finite element-type method is proposed for the Helmholtz equation. The basis employed consists of elementwise smooth elementary solutions to the Helmholtz equation and hence are not polynomials. A convergence analysis is given as well as numerical tests.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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