On different finite element methods for approximating the gradient of the solution to the helmholtz equation
Haslinger, J., Neittaanmäki, P. (1984). On different finite element methods for approximating the gradient of the solution to the helmholtz equation. Computer Methods in Applied Mechanics and Engineering, 42 (2), 131-148. doi:10.1016/0045-7825(84)90022-7
We consider the numerical solution of the Helmholtz equation by different finite element methods. In particular, we are interested in finding an efficient method for approximating the gradient of the solution. We first approximate the gradient by the standard Ritz-Galerkin method. As a second method a two-stage method due to Aziz and Werschulz (1980) is presented. It is shown that this method gives the same accuracy in the computed gradient and in the computed solution also in the nonconforming case. Finally, a direct method with asymptotic error estimates is given. It turns out that the presented direct method is of lowest computational complexity. Test examples are presented to illustrate the accuracy of the methods.
MetadataShow full item record
Showing items with similar title or keywords.
Neittaanmäki, Pekka; Saranen, Jukka (Springer, 1981)A nonconforming mixed finite element method is presented for approximation of ∇w with Δw=f,w| r =0. Convergence of the order∥∇w−uh∥0,Ω=O(h2) is proved, when linear finite elements are used. Only the standard regularity ...
Mönkölä, Sanna (University of Jyväskylä, 2008)
Airaksinen, Tuomas; Toivanen, Jari (Elsevier, 2013)A new method is presented to obtain a local active noise control that is optimal in stochastic environment. The method uses numerical acoustical modeling that is performed in the frequency domain by using a sequence of ...
Křižek, Michal; Neittaanmäki, Pekka (Springer, 1984)We study a superconvergence phenomenon which can be obtained when solving a 2nd order elliptic problem by the usual linear elements. The averaged gradient is a piecewise linear continuous vector field, the value of which ...
Neittaanmäki, Pekka (Wiley, 1983)