Geodesic
Approximating the volume integral by a surface integral via the divergence theorem
Silvestru Sever Dragomir1
1 Mathematics, 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 <a href="http://rgmia.org/dragomir">http://rgmia.org/dragomir</a>
Applicationes Mathematicae, Tome 47 (2020) no. 1, pp. 75-98.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/am2393-1-2020
Keywords: utilising divergence theorem n dimensional integrals provide error estimates approximating integral body nbsp bounded closed subset mathbb geq smooth piecewise smooth boundary partial integral surface partial other simple terms examples dimensional given

Silvestru Sever Dragomir 1

1 Mathematics, 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 <a href="http://rgmia.org/dragomir">http://rgmia.org/dragomir</a> 
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Silvestru Sever Dragomir. Approximating the volume integral by a surface integral via the divergence theorem. Applicationes Mathematicae, Tome 47 (2020) no. 1, pp. 75-98. doi : 10.4064/am2393-1-2020. http://geodesic.mathdoc.fr/articles/10.4064/am2393-1-2020/

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