Lines Matching refs:vector

20 …vector velocity field), $E$ the total energy density (defined as $E = \rho e$, where $e$ is the to…
28 The system {eq}`eq-ns` can be rewritten in vector form
32 $$ (eq-vector-ns)
34 for the state variables 5-dimensional vector
85 To obtain a finite element discretization, we first multiply the strong form {eq}`eq-vector-ns` by …
102 $$ (eq-weak-vector-ns)
171 We solve {eq}`eq-weak-vector-ns` using a Galerkin discretization (default) or a stabilized method, …
178 …ighted residual of the strong form {eq}`eq-vector-ns` is added to the Galerkin formulation {eq}`eq…
190   $$ (eq-weak-vector-ns-supg)
196 …This method is a simplified version of *SUPG* {eq}`eq-weak-vector-ns-supg` which is developed for …
206   $$ (eq-weak-vector-ns-su)
210 In both {eq}`eq-weak-vector-ns-su` and {eq}`eq-weak-vector-ns-supg`, $\bm\tau \in \mathbb R^{5\time…
228 A velocity vector $\bm u$ can be pulled back to the reference element as $\bm u_{\bm X} = \nabla_{\…
232 A contravariant measure of element length in the direction of a unit vector $\hat{\bm n}$ is given …
316 …rted to be optimal at 0.5 for linear elements, $\hat{\bm n}_i$ is a unit vector in direction $i$, …
337 {ref}`problem-advection`, the problem of the transport of energy in a uniform vector velocity field…
341 The strong residual in the SUPG operator in {eq}`eq-weak-vector-ns-supg` and {eq}`eq-weak-vector-ns…
395 $$ (eq-vector-les)