Lines Matching refs:text

59 \end{pmatrix}}_{\bm F_{\text{adv}}} +
64 \end{pmatrix}}_{\bm F_{\text{diff}}},\\
186 …+ \int_{\Omega} \nabla\bm v \tcolon\left(\frac{\partial \bm F_{\text{adv}}}{\partial \bm q}\right)…
203 …+ \int_{\Omega} \nabla\bm v \tcolon\left(\frac{\partial \bm F_{\text{adv}}}{\partial \bm q}\right)…
211 The SUPG technique and the operator $\frac{\partial \bm F_{\text{adv}}}{\partial \bm q}$ (rather th…
212 The forward variational form can be readily expressed by differentiating $\bm F_{\text{adv}}$ of {e…
216 \diff\bm F_{\text{adv}}(\diff\bm q; \bm q) &= \frac{\partial \bm F_{\text{adv}}}{\partial \bm q} \d…
313 \tau_{ii} = c_{\tau} \frac{2 \xi(\mathrm{Pe})}{(\lambda_{\max \text{abs}})_i \lVert \nabla_{x_i} \b…
317 …\bm F_{\text{adv}}}{\partial \bm q} \cdot \hat{\bm n}_i$ in each direction $i$ is a $5\times 5$ ma…
329 \lambda_{\max \text{abs}} \Bigl( \frac{\partial \bm F_{\text{adv}}}{\partial \bm q} \cdot \hat{\bm …
341 …g` and {eq}`eq-weak-vector-ns-su` features the term $\nabla \cdot \bm F_{\text{diff}}(\bm{q}_N)$, …
342 …ative to evaluate; first to evaluate $\bm \sigma$ and $\nabla T$ for $F_{\text{diff}}$, the second…
345 … (optionally) perform a projection operation to get $\nabla \cdot \bm F_{\text{diff}}(\bm{q}_N)$ a…
352 Here, $\bm F_{\text{diff}}$ is $L^2$ projected onto the finite element space and then the divergenc…
353 For linear basis functions, this leads to constant values of $\nabla \cdot \bm F_{\text{diff}}$ wit…
360 …ction of the divergence of the diffusive flux itself, $\nabla \cdot \bm F_{\text{diff}}(\bm{q}_N)$.
361 Then $\nabla \cdot \bm F_{\text{diff}}$ itself is a function on the finite element space and can be…
363 To do this, look at the RHS of the $L^2$ projection of $\nabla \cdot \bm F_{\text{diff}}(\bm{q}_N)$:
366 \int_{\Omega} \bm v \cdot \nabla \cdot \bm F_{\text{diff}}(\bm{q}_N) \,dV
369 As noted, we can't calculate $\nabla \cdot \bm F_{\text{diff}}(\bm{q}_N)$ at quadrature points, so …
372 \int_{\partial \Omega} \bm v \cdot \bm{F}_{\text{diff}}(\bm q_N) \cdot \widehat{\bm{n}} \,dS
373 - \int_{\Omega} \nabla \bm v \!:\! \bm{F}_{\text{diff}}(\bm{q}_N)\,dV
377 After the projection, $\nabla \cdot \bm F_{\text{diff}}(\bm{q}_N)$ is interpolated directly to quad…