# 2D formulation for Electrostatic Problems

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== 2D formulation for Triangular Elements == | == 2D formulation for Triangular Elements == | ||

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

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

− | \frac{\partial N_1}{\partial x} & \frac{\partial N_2}{\partial x} & \frac{\partial N_3}{\partial x}\\ | + | \displaystyle \frac{\partial N_1}{\partial x} & \frac{\partial N_2}{\partial x} & \frac{\partial N_3}{\partial x}\\ |

\, \\ | \, \\ | ||

− | \frac{\partial N_1}{\partial y} & \frac{\partial N_2}{\partial y} & \frac{\partial N_3}{\partial y} | + | \displaystyle \frac{\partial N_1}{\partial y} & \frac{\partial N_2}{\partial y} & \frac{\partial N_3}{\partial y} |

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

</math> | </math> |

## Revision as of 19:19, 11 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