The effect of numerical integration on the finite element approximation of linear functionals

@article{Babuska2011TheEO,
  title={The effect of numerical integration on the finite element approximation of linear functionals},
  author={Ivo Babuska and Uday Banerjee and Hengguang Li},
  journal={Numerische Mathematik},
  year={2011},
  volume={117},
  pages={65-88}
}
In this paper, we have studied the effect of numerical integration on the finite element method based on piecewise polynomials of degree k, in the context of approximating linear functionals, which are also known as “quantities of interest”. We have obtained the optimal order of convergence, $${\mathcal{O}(h^{2k})}$$, of the error in the computed functional, when the integrals in the stiffness matrix and the load vector are computed with a quadrature rule of algebraic precision 2k − 1. However… 
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