The phrase "using the divergence theorem" is correct and usable in written English.
You can use it when discussing the application of the divergence theorem, which is a mathematical concept that relates the flux of a vector field through a closed surface to the divergence of the vector field within that surface. It is often used in physics, engineering, and other scientific fields. Example: "We can calculate the flux of the electric field through the surface using the divergence theorem, as it relates the electric charge within the surface to the flux through that surface."
Using the divergence theorem, the method transforms the domain integral into integrals evaluated over the facets of the polyhedra.
The strain matrices are modified with a linear smoothing technique by using the divergence theorem between the nodal shape functions and their derivatives in Taylor's expansion.
For the last integral over G, considering the integral of the inequality (2.4) by using the divergence theorem and in view of (3.13) implies that (M[u]leq0).
In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem.
Using the divergence theorem we have Q γ ( f ) : = ∫ Ω γ | ∇ u | 2 d x = ∫ ∂ Ω Λ γ ( f ) f d S (4 where d S denotes surface measure and u is the solution of (2).
On the other hand, (F P) i does not converge, pointwise or uniformly, to R T. Instead, it converges weakly to R T. This can be easily demonstrated using the divergence theorem.
end{aligned} (33) We integrate equation (33) over B, use the divergence theorem and equation (11) to obtain the final result.
end{aligned} (25) We integrate this relation over (Btimes [0,t]), (tin [0,T)), and use the divergence theorem and equation (12) to obtain equation (19).
end{aligned} (22) We integrate this relation over (Btimes [0,t]), (tin [0,T)), and use the divergence theorem and equation (11) to obtain equation (18). We have frac{partial }{partial s} biggl{ frac{1}{2}frac{1}{theta_{0}}c theta^{2}(s) biggr} = theta (s)frac{1}{theta_{0}}c dot{theta }(s).
where we have used the divergence theorem along with ϕ=0 on ∂ Ω to arrive at the first and last equalities, and the uniform convergence of (tilde {boldsymbol {x}}^{i}) to interchange the limit and the integral signs in the first equality.
end{aligned} (27) We integrate this relation over (Btimes [0,t]), (tin [0,T)), and use the divergence theorem and equation (13) to obtain equation (20). □. Let us consider a solution of the initial boundary value problem corresponding to the external data (mathcal{D}).
