Approximating the volume integral by a surface integral via the divergence theorem

Volume 47 / 2020

Silvestru Sever Dragomir Applicationes Mathematicae 47 (2020), 75-98 MSC: Primary 26D15. DOI: 10.4064/am2393-1-2020 Published online: 10 June 2020

Abstract

By utilising the divergence theorem for $n$-dimensional integrals, we provide some error estimates for approximating the integral on a body $B,$ a bounded closed subset of $\mathbb {R}^{n}$ $(n\geq 2)$ with smooth (or piecewise smooth) boundary $\partial B,$ by an integral on the surface $\partial B$ and some other simple terms. Some examples in the $3$-dimensional case are also given.

Authors

  • Silvestru Sever DragomirMathematics, College of Engineering & Science
    Victoria University
    PO Box 14428
    Melbourne, MC 8001, Australia
    and
    DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences
    School of Computer Science & Applied Mathematics
    University of the Witwatersrand
    Private Bag 3
    Johannesburg 2050, South Africa
    ORCID: 0000-0003-2902-6805
    http://rgmia.org/dragomir
    e-mail

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