Vector calculus operators for the symbolic form

[valentinsulzer]

(Opening a separate issue from SciML/DiffEqOperators.jl#153 SciML/DiffEqOperators.jl#146 which are about the lazy operators)

Add vector calculus operators (Laplacian, Divergence, Gradient) to supplement the Differential operator.

This would enable writing equations in generic form, with the geometry then specified later by the domains (also need to consider boundary conditions in this case). Some sample code for Poisson:

@parameters x y
@variables u(..)
Δ = Laplacian(x,y)

# 2D PDE
eq  = Δ(u(x,y)) ~ -sin(pi*x)*sin(pi*y)

One possible way to implement this is to have a @rule which replaces the vector calculus operators with the appropriate Differential operators (based on the type of the domains) and then reuse the existing MOLFiniteDifference code.
For non-Cartesian geometries, this requires at least SciML/DiffEqOperators.jl#354 , and probably a bunch of other stuff (e.g. how do you implement finite differences at r=0).

[valentinsulzer]

Then later on we can do some cool stuff like automatically generating weak forms for Gridap

[valentinsulzer]

Where would be the place to first define this? ModelingToolkit.jl? Symbolics.jl?

[ChrisRackauckas]

I think it would be good to add these operators into Symbolics.jl and then use them in MTK's interface.