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A variational multiscale method with subscales on the element boundaries for the Helmholtz equation
Author(s) -
Baiges Joan,
Codina Ramon
Publication year - 2012
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4406
Subject(s) - helmholtz equation , finite element method , galerkin method , mathematics , helmholtz free energy , discontinuous galerkin method , mathematical analysis , expression (computer science) , moving least squares , boundary value problem , computer science , physics , structural engineering , engineering , programming language , quantum mechanics
SUMMARY In this paper, we apply the variational multiscale method with subgrid scales on the element boundaries to the problem of solving the Helmholtz equation with low‐order finite elements. The expression for the subscales is obtained by imposing the continuity of fluxes across the interelement boundaries. The stabilization parameter is determined by performing a dispersion analysis, yielding the optimal values for the different discretizations and finite element mesh configurations. The performance of the method is compared with that of the standard Galerkin method and the classical Galerkin least‐squares method with very satisfactory results. Some numerical examples illustrate the behavior of the method. Copyright © 2012 John Wiley & Sons, Ltd.