# 2D formulation for Electrostatic Problems

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::<math> | ::<math> | ||

\mathbf{B}= | \mathbf{B}= | ||

− | = | + | = |

− | \frac{1}{2 A^{(e) | + | \frac{1}{2 A^{(e)}} |

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

- y_1 + y_3 & - y_2 + y_1 \\ | - y_1 + y_3 & - y_2 + y_1 \\ | ||

Line 226: | Line 226: | ||

-1 & 0 & 1 | -1 & 0 & 1 | ||

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

− | = | + | = |

− | \frac{1}{2 A^{(e) | + | \frac{1}{2 A^{(e)}} |

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

- y_3 + y_2 & - y_1 + y_3 & - y_2 + y_1 \\ | - y_3 + y_2 & - y_1 + y_3 & - y_2 + y_1 \\ |

## Revision as of 18:12, 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)}