FEM EquationElectrostatic

This equation perform electrostatic analyses using Gauss' law.

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

Usage

 * 1) After adding an Elmer solver as described here, select it in the tree view.
 * 2) Now either use the toolbar button [[Image:FEM_EquationElectrostatic.svg|24px]] or the menu.
 * 3) 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 electrostatic equation provides these special settings:
 * : Calculates the capacitance matrix. The matrix contains the the point charges of the mesh knots.
 * : Calculates the electric energy.
 * : Calculates the electric field.
 * : Calculates the electric flux.
 * : Calculates the surface charge.
 * : File in which the capacitance matrix is being saved. It is only used if is set to true.
 * : If constant weighting for results is used.
 * : Potential difference in Volt for which the capacitance is calculated. It is only used if is set to false. Therefore in fact this setting specifies the voltage between the electrodes of a simple capacitor. Note that the given voltage has to be consistent with the potentials defined in the boundary conditions.

Constraint Information
The electrostatic equation takes the following constraints into account if they are set:


 * [[Image:FEM_ConstraintElectrostaticPotential.svg|32px]] Electrostatic potential constraint
 * [[Image:FEM_ConstantVacuumPermittivity.svg|32px]] Constant vacuum permittivity

Note
Except for calculations in 2D, for electrostatic potential constraints it is important that they act on a face or body. Constraints for 3D set to lines or vertices are not recognized by the Elmer solver.

Results
The available results depend on the solver settings. If none of the settings was set to true, only the electric force density and the electric potential are calculated. Otherwise also the corresponding results will be available.

The possible results are:
 * Electric energy density in $$\rm J/m^3$$
 * Electric field in $$\rm V/m$$
 * Electric flux in $$\rm A\cdot s/m^2$$
 * Electric force density in $$\rm N/m^2$$
 * Potential in $$\rm V$$
 * Potential loads in $$\rm C$$