FEM EquationFlux/pl

This equation is used to calculate the fluxes resulting usually from Poisson kind of equations. These include the Heat equation and the  Electrostatic equation.

For info about the math of the equation, see the Elmer models manual, section Flux Computation.

Usage

 * 1) After adding an Elmer solver as described here, select it in the tree view.
 * 2) Either use the toolbar button [[Image:FEM_EquationFlux.svg|24px]] or the menu.
 * 3) Now either add a heat equation  (toolbar button [[Image:FEM_EquationHeat.svg|24px]] or menu ) or an electrostatic equation (toolbar button [[Image:FEM_EquationElectrostatic.svg|24px]] or menu ). This is important because the flux equation needs the constraints set for these equastions.
 * 4) When using the electrostatic equation, change the property  to None. and the property  to Potential.
 * 5) Change the equation's solver settings or the general solver settings if necessary.

Solver Settings
For the general solver settings, see the Elmer solver settings.

The flux equation provides these special settings:
 * : If true, continuity is enforced within the same material in the discontinuous Galerkin discretization using the penalty terms of the discontinuous Galerkin formulation.
 * : Calculates the flux vector.
 * : Calculates the absolute of the flux vector. Requires that is true.
 * : Computes the magnitude of the vector field. Requires that  is true. Basically it is the same as  but this requires less memory because it solves the matrix equation only once. The downside is that negative values may be introduced.
 * : Calculates the gradient of the flux.
 * : Calculates the absolute flux gradient. Requires that is true.
 * : Computes the magnitude of the vector field. Requires that is true. Basically it is the same as  but this requires less memory because it solves the matrix equation only once. The downside is that negative values may be introduced.
 * : For discontinuous fields the standard Galerkin approximation enforces continuity which may be unphysical. As a remedy for this, set this property to true. Then the result may be discontinuous and may even be visualized as such.
 * : If true, the negative values of the computed magnitude fields are set to zero.
 * : Name of the proportionality coefficient to compute the flux.
 * : Name of the potential variable used to compute the gradient.

Constraint Information
The flux equation does not have own constraints. It takes the constraints from the Heat equation or the  Electrostatic equation.

Results
The available results depend on the solver settings. If none of them was set to true, nothing is calculated. Otherwise also the corresponding results will be available.

The resulting flux is either the heat flux $$\rm W/m^2$$ (misleadingly named "temperature flux") or the potential flux in $$\rm W/m^2$$ ($$\rm A\cdot V/m^2$$).