Default to Lagrange{refdim,refshape,1}() for geometric mapping
#695
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This patch changes the default value for the geometric mapping in
`(Cell|Face)(Scalar|Vector)Values` to linear Lagrange interpolation
instead of (re)using the function interpolation. This decouples these
two concepts further.
Some "real world" examples where I think this new default is more sane,
and the current default is just a stumbling block:
1. Consider the following code with linear cells:
```julia
grid = generate_grid(Triangle, ...)
ip = Lagrange{2, RefTriangle, 1}()
cv = CellVectorValues(qr, ip)
```
To update this to use e.g. a quadratic approximation one currently
have to change more than just the approximation order, i.e. one has
to use
```julia
grid = generate_grid(Triangle, ...)
ip = Lagrange{2, RefTriangle, 2}()
ipg = Lagrange{2, RefTriangle, 1}()
cv = CellVectorValues(qr, ip, ipg)
```
instead of simply
```julia
grid = generate_grid(Triangle, ...)
ip = Lagrange{2, RefTriangle, 2}()
cv = CellVectorValues(qr, ip)
```
2. For the Taylor-Hood element one *always* have to worry about the
geometric mapping, regardless if it is linear or quadratic:
```julia
ip_g = Lagrange{2, RefTriangle, 1}()
ip_u = Lagrange{2, RefTriangle, 2}()
ip_p = Lagrange{2, RefTriangle, 1}()
cv_u = CellVectorValues(qr, ip_u, ip_g)
cv_p = CellVectorValues(qr, ip_p, ip_g)
```
instead of just
```julia
ip_u = Lagrange{2, RefTriangle, 2}()
ip_p = Lagrange{2, RefTriangle, 1}()
cv_u = CellVectorValues(qr, ip_u)
cv_p = CellVectorValues(qr, ip_p)
```
3. For more exotic elements, such as `VectorizedInterpolation` (#694),
or `RaviartThomas` it is also a more useful default.
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This patch changes the default value for the geometric mapping in
(Cell|Face)(Scalar|Vector)Valuesto linear Lagrange interpolationinstead of (re)using the function interpolation. This decouples these
two concepts further.
Some "real world" examples where I think this new default is more sane,
and the current default is just a stumbling block:
Consider the following code with linear cells:
To update this to use e.g. a quadratic approximation one currently
have to change more than just the approximation order, i.e. one has
to use
instead of simply
For the Taylor-Hood element one always have to worry about the
geometric mapping, regardless if it is linear or quadratic:
instead of just
For more exotic elements, such as
VectorizedInterpolation(Implement(Scalar|Vector)InterpolationandVectorizedInterpolation{<:ScalarInterpolation}#694),or
RaviartThomasit is also a more useful default.