Summary
Finite element approximations of the eigenpairs of differential operators are computed as eigenpairs of matrices whose elements involve integrals which must be evaluated by numerical integration. The effect of this numerical integration on the eigenvalue and eigenfunction error is estimated. Specifically, for 2nd order selfadjoint eigenvalue problems we show that finite element approximations with quadrature satisfy the well-known estimates for approximations without quadrature, provided the quadrature rules have appropriate degrees of precision.
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The work of this author was partially supported by the National Science Foundation under Grant DMS-84-10324
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Banerjee, U., Osborn, J.E. Estimation of the effect of numerical integration in finite element eigenvalue approximation. Numer. Math. 56, 735–762 (1989). https://doi.org/10.1007/BF01405286
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DOI: https://doi.org/10.1007/BF01405286