Classes | Functions
elliptic::dg::NumericalFluxes Namespace Reference

Numerical fluxes for elliptic systems. More...


struct  FirstOrderInternalPenalty
 The internal penalty flux for first-order elliptic equations. More...
struct  FirstOrderInternalPenalty< Dim, FluxesComputerTag, tmpl::list< FieldTags... >, tmpl::list< AuxiliaryFieldTags... > >


DataVector penalty (const DataVector &element_size, const size_t num_points, const double penalty_parameter) noexcept
 The penalty factor in internal penalty fluxes. More...

Detailed Description

Numerical fluxes for elliptic systems.

Function Documentation

◆ penalty()

DataVector elliptic::dg::NumericalFluxes::penalty ( const DataVector element_size,
const size_t  num_points,
const double  penalty_parameter 

The penalty factor in internal penalty fluxes.

The penalty factor is computed as

\begin{equation} \sigma = C \frac{N_\text{points}^2}{h} \end{equation}

where \(N_\text{points} = 1 + N_p\) is the number of points (or one plus the polynomial degree) and \(h\) is a measure of the element size. Both quantities are taken perpendicular to the face of the DG element that the penalty is being computed on. \(C\) is the penalty parameter.

See also
elliptic::dg::NumericalFluxes::FirstOrderInternalPenalty for details