divergence theorem


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divergence theorem

[də′vər·jəns ‚thir·əm]
(mathematics)
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We need to consider divergence theorem; to be more explicit we need the Green's identity of the first kind, in order to resolve the right-hand side of this equation.
If [omega] [member of] [H.sup.1]([R.sup.3]) [intersection] ([R.sup.3]), then the divergence theorem andtrace theorem induce the following estimates:
The boundary of B, denoted by [partial derivative]B, is a sufficiently smooth surface to admit the application of divergence theorem. The closure of B will be denoted by [bar.B].
Integrating (16) over the volume V (assumed to contain the electron core (-[e.sub.*], m)), and using the divergence theorem, leads to [1, p.
Mimetic finite difference (MFD) approximations to differential vector operators along with compatible inner products satisfy a discrete analog of the Gauss divergence theorem. On nodal grids, an important MFD family comprises the summation-by-part (SBP) difference operators, whose development and initial applications were focused on the conservative discretization of wave propagation problems [22, 23, 24, 30].
By application of the Gauss divergence theorem to the tetrahedron, one can write:
In sections on vector analysis, complex analysis, and Fourier analysis, they consider such topics as gradient vector fields, the divergence theorem, complex integration, Fourier series, and applications to ordinary and partial differential equations.
Numerical integration using the Divergence Theorem in the coordinates ([theta], [phi]).
integrate over [OMEGA], and use the divergence theorem.
THE DIVERGENCE THEOREM AND SETS OF FINITE PERIMETER.
As a result, the approach chosen for this study was based on a fundamental theorem in calculus, called the Divergence Theorem (see Taylor (2)), an analogue of Green's Theorem in two dimensional space.