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Evaluate flux of PDE solution

```
[cgradx,cgrady]
= evaluateCGradient(results,xq,yq)
```

```
[cgradx,cgrady,cgradz]
= evaluateCGradient(results,xq,yq,zq)
```

`[___] = evaluateCGradient(results,querypoints)`

`[___] = evaluateCGradient(___,iU)`

`[___] = evaluateCGradient(___,iT)`

```
[cgradx,cgrady]
= evaluateCGradient(results)
```

```
[cgradx,cgrady,cgradz]
= evaluateCGradient(results)
```

`[___] = evaluateCGradient(`

returns the flux of PDE solution for the stationary equation at the 2-D or 3-D
points specified in `results`

,`querypoints`

)`querypoints`

.

`[___] = evaluateCGradient(___,`

returns the flux of the solution of the PDE system for equation indices
(components) `iU`

)`iU`

. When evaluating flux for a system of PDEs,
specify `iU`

after the input arguments in any of the previous
syntaxes.

The first dimension of `cgradx`

,
`cgrady`

, and, in the 3-D case,
`cgradz`

corresponds to query points. The second
dimension corresponds to equation indices `iU`

.

`[___] = evaluateCGradient(___,`

returns the flux of PDE solution for the time-dependent equation or system of
time-dependent equations at times `iT`

)`iT`

. When evaluating flux
for a time-dependent PDE, specify `iT`

after the input
arguments in any of the previous syntaxes. For a system of time-dependent PDEs,
specify both equation indices (components) `iU`

and time
indices `iT`

.

The first dimension of `cgradx`

,
`cgrady`

, and, in the 3-D case,
`cgradz`

corresponds to query points. For a single
time-dependent PDE, the second dimension corresponds to time-steps
`iT`

. For a system of time-dependent PDEs, the second
dimension corresponds to equation indices `iU`

, and the third
dimension corresponds to time-steps `iT`

.

`[`

returns the flux of PDE solution of a 2-D problem at the nodal points of the
triangular mesh. The shape of output arrays, `cgradx`

,`cgrady`

]
= evaluateCGradient(`results`

)`cgradx`

and
`cgrady`

, depends on the number of PDEs for which
`results`

is the solution. The first dimension of
`cgradx`

and `cgrady`

represents the
node indices. For a system of stationary or time-dependent PDEs, the second
dimension represents equation indices. For a single time-dependent PDE, the
second dimension represents time-steps. The third dimension represents time-step
indices for a system of time-dependent PDEs.

`[`

returns the flux of PDE solution of a 3-D problem at the nodal points of the
tetrahedral mesh. The first dimension of `cgradx`

,`cgrady`

,`cgradz`

]
= evaluateCGradient(`results`

)`cgradx`

,
`cgrady`

, and `cgradz`

represents the
node indices. The second dimension represents the equation indices. For a system
of stationary or time-dependent PDEs, the second dimension represents equation
indices. For a single time-dependent PDE, the second dimension represents
time-steps. The third dimension represents time-step indices for a system of
time-dependent PDEs.

While the

`results`

object contains the solution and its gradient (both calculated at the nodal points of the triangular or tetrahedral mesh), it does not contain the flux of the PDE solution. To compute the flux at the nodal locations, call`evaluateCGradient`

without specifying locations. By default,`evaluateCGradient`

uses nodal locations.

`PDEModel`

| `StationaryResults`

| `TimeDependentResults`

| `evaluateGradient`

| `interpolateSolution`