# 2D formulation for Electrostatic Problems

Line 47: | Line 47: | ||

N_n | N_n | ||

\end{bmatrix} | \end{bmatrix} | ||

− | + | \qquad | |

− | + | \mathbf{a} = | |

− | + | ||

\begin{bmatrix} | \begin{bmatrix} | ||

a_1 \\ | a_1 \\ |

## Revision as of 15:01, 30 October 2009

The 2D Electrostatic Poisson's equation given by the governing PDE and its boundary conditions:

can be written as (see the General formulation for Electrostatic Problems):

with:

This is:

with the infinit condition factor and the field produced whe is fixed by .

The weak form of this expression can be obtained using the integration by parts. In addition, if :

Remembering that:

is the gradient potential with:

and:

The electric field and electric displacement field can be written as follows:

We will now use the Galerkin Method . So, finally, the integral expression ready to create the matricial system of equations is:

Note that **K** is a coefficients matrix that depends on the geometrical and physical properties of the problem, **a** is the vector with the * n* unknowns to be obtained and

**f**is a vector that depends on the source values and boundary conditions.