# 2D formulation for Electrostatic Problems

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::<math>\mathbf{f}^{(e)}= | ::<math>\mathbf{f}^{(e)}= | ||

− | \int_{\Omega^{(e)}} \mathbf{N^T} \ | + | \int_{\Omega^{(e)}} \mathbf{N^T} \rho_S \partial \Omega^{(e)} - |

\oint_{\Gamma_q^{(e)}} \mathbf{N^T} \bar D_n \partial \Gamma_q^{(e)} - | \oint_{\Gamma_q^{(e)}} \mathbf{N^T} \bar D_n \partial \Gamma_q^{(e)} - | ||

\oint_{\Gamma_V^{(e)}} \mathbf{n^T} \mathbf{N^T} \mathbf{q_n} \partial \Gamma_V^{(e)} | \oint_{\Gamma_V^{(e)}} \mathbf{n^T} \mathbf{N^T} \mathbf{q_n} \partial \Gamma_V^{(e)} |

## Revision as of 15:25, 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 (* n* is the number of nodes of the element):