Lines Matching refs:v

85 …e first multiply the strong form {eq}`eq-vector-ns` by a test function $\bm v \in H^1(\Omega)$ and…
88 …} \bm v \cdot \left(\frac{\partial \bm{q}_N}{\partial t} + \nabla \cdot \bm{F}(\bm{q}_N) - \bm{S}(…
91 with $\mathcal{V}_p = \{ \bm v(\bm x) \in H^{1}(\Omega_e) \,|\, \bm v(\bm x_e(\bm X)) \in P_p(\bm{I…
97 \int_{\Omega} \bm v \cdot \left( \frac{\partial \bm{q}_N}{\partial t} - \bm{S}(\bm{q}_N) \right)  \…
98 - \int_{\Omega} \nabla \bm v \!:\! \bm{F}(\bm{q}_N)\,dV & \\
99 + \int_{\partial \Omega} \bm v \cdot \bm{F}(\bm q_N) \cdot \widehat{\bm{n}} \,dS
100   &= 0 \, , \; \forall \bm v \in \mathcal{V}_p \,,
107 …v \!:\! \bm F$ represents contraction over both fields and spatial dimensions while a single dot r…
183 …\int_{\Omega} \bm v \cdot \left( \frac{\partial \bm{q}_N}{\partial t} - \bm{S}(\bm{q}_N) \right)  …
184   - \int_{\Omega} \nabla \bm v \!:\! \bm{F}(\bm{q}_N)\,dV & \\
185   + \int_{\partial \Omega} \bm v \cdot \bm{F}(\bm{q}_N) \cdot \widehat{\bm{n}} \,dS & \\
186 …+ \int_{\Omega} \nabla\bm v \tcolon\left(\frac{\partial \bm F_{\text{adv}}}{\partial \bm q}\right)…
188   \, , \; \forall \bm v \in \mathcal{V}_p
200 …\int_{\Omega} \bm v \cdot \left( \frac{\partial \bm{q}_N}{\partial t} - \bm{S}(\bm{q}_N) \right)  …
201   - \int_{\Omega} \nabla \bm v \!:\! \bm{F}(\bm{q}_N)\,dV & \\
202   + \int_{\partial \Omega} \bm v \cdot \bm{F}(\bm{q}_N) \cdot \widehat{\bm{n}} \,dS & \\
203 …+ \int_{\Omega} \nabla\bm v \tcolon\left(\frac{\partial \bm F_{\text{adv}}}{\partial \bm q}\right)…
204   & = 0 \, , \; \forall \bm v \in \mathcal{V}_p
254 \nabla v \cdot \bm u \tau \bm u \cdot \nabla q = \nabla_{\bm X} v \cdot (\bm u_{\bm X} \tau \bm u_{…
366 \int_{\Omega} \bm v \cdot \nabla \cdot \bm F_{\text{diff}}(\bm{q}_N) \,dV
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
515 \bm{u}(\bm{x}, t) = \bm{\overline{u}}(\bm{x}) + \bm{C}(\bm{x}) \cdot \bm{v}'
520 \bm{v}' &= 2 \sqrt{3/2} \sum^N_{n=1} \sqrt{q^n(\bm{x})} \bm{\sigma}^n \cos(\kappa^n \bm{d}^n \cdot …