calculus

derivative!(df, f, coord, spectral)

Non-upwinding derivative.

derivative!(df, f, coord, adv_fac, spectral)

Upwinding derivative.

maps the derivative at points away from element boundaries from the grid/element representation to the full grid representation

elementwise_derivative!(coord, f, adv_fac, spectral)
elementwise_derivative!(coord, f, spectral)

Generic function for element-by-element derivatives

First signature, with adv_fac, calculates an upwind derivative, the second signature calculates a derivative without upwinding information.

Result is stored in coord.scratch_2d.

Computes the integral of the 3D integrand, using the input wgts

Computes the integral of the integrand multiplied by v^n, using the input wgts

Computes the integral of the 2D integrand, using the input wgts

Computes the integral of the integrand multiplied by v, using the input wgts

Computes the integral of the integrand, using the input wgts

mass_matrix_solve!(f, b, spectral::weak_discretization_info)

Solve

\[M.f = b\]

for $a$, where $M$ is the mass matrix of a weak-form finite element method and $b$ is an input.

if at the boundary point within the element, must carefully choose which value of df to use; this is because df is multi-valued at the overlapping point at the boundary between neighboring elements. here we choose to use the value of df from the upwind element.