# 2D formulation for Electrostatic Problems

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− | \frac{\partial N_1}{\partial \alpha}=-1 \qquad \frac{\partial N_2}{\partial \alpha}=1 \qquad \frac{\partial N_3}{\partial \alpha}=0 | + | \frac{\partial N_1}{\partial \alpha}=-1 \qquad |

− | + | \frac{\partial N_2}{\partial \alpha}=1 \qquad | |

− | + | \frac{\partial N_3}{\partial \alpha}=0 \qquad | |

− | + | \frac{\partial N_1}{\partial \beta}=-1 \qquad | |

− | \frac{\partial N_1}{\partial \beta}=-1 \qquad \frac{\partial N_2}{\partial \beta}=0 | + | \frac{\partial N_2}{\partial \beta}=0 \qquad |

+ | \frac{\partial N_3}{\partial \beta}=1 | ||

</math> | </math> | ||

## Revision as of 18:04, 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)}