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Mass-lumping or not mass-lumping for eigenvalue problems. (English) Zbl 1041.65086

The authors analyze the effect of mass-lumping in the linear triangular finite element approximation of second-order positive definite elliptic eigenvalue problems. They prove that the eigenvalue obtained by using mass-lumping is not greater than the one obtained with exact integration. For singular eigenfunctions, as those arizing in non convex polygons they prove that the eigenvalue obtained with mass-lumping is not less than the exact eigenvalue, when the meshsize is small enough. The conclusion is that the mass-lumping is convenient in the singular case. When the eigenfunction is smooth, the authors show on several numerical experiments that the eigenvalue computed with mass-lumping is below the exact one if the mesh is not too coarse.

MSC:

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35P15 Estimates of eigenvalues in context of PDEs
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References:

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