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Quadrature and Schatz’s Pointwise Estimates for Finite Element Methods

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Abstract

We investigate numerical integration effects on weighted pointwise estimates. We prove that local weighted pointwise estimates will hold, modulo a higher order term and a negative-order norm, as long as we use an appropriate quadrature rule. To complete the analysis in an application, we also prove optimal negative-order norm estimates for a corner problem taking into account quadrature. Finally, we present an example to show that our result is sharp.

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Authors and Affiliations

  1. Center for Applied Mathematics, Cornell University, 657 Rhodes Hall, Ithaca, NY, 14853, USA

    J. Guzmán

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  1. J. Guzmán
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Correspondence to J. Guzmán.

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AMS subject classification (2000)

65N15

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Guzmán, J. Quadrature and Schatz’s Pointwise Estimates for Finite Element Methods. Bit Numer Math 45, 695–707 (2005). https://doi.org/10.1007/s10543-005-0029-9

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  • DOI: https://doi.org/10.1007/s10543-005-0029-9

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