# 2D formulation for Electrostatic Problems

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= | = | ||

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

− | 1-\alpha-\beta & \alpha & \beta | + | (1-\alpha-\beta) & \alpha & \beta |

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

\qquad | \qquad |

## Revision as of 19:26, 12 November 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 (* n* is the number of nodes of the element):

## 2D formulation for Triangular Elements

After applying the numerical integration for triangular elements by using the natural coordinates, we obtain:

### Stiffness Matrix K^{(e)}

### Source Vector f^{(e)}