abstract type DiffOp end

function apply(D::DiffOp, v::AbstractVector) where N
    error("not implemented")
end

function innerProduct(D::DiffOp, u::AbstractVector, v::AbstractVector)::Real
    error("not implemented")
end

function matrixRepresentation(D::DiffOp)
    error("not implemented")
end

function boundaryCondition(D::DiffOp)
    error("not implemented")
end

function interface(Du::DiffOp, Dv::DiffOp, b::BoundaryID; type)
    error("not implemented")
end


# Differential operator for a*d^2/dx^2
struct Laplace1D <: DiffOp
    grid
    a
    op
end

function apply(L::Laplace, v::AbstractVector)::AbstractVector

end