# 2D formulation for Electrostatic Problems

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\int_{\Omega} \mathbf{B^T} \mathbf{\varepsilon} \mathbf{B} \mathbf{a} \partial \Omega + | \int_{\Omega} \mathbf{B^T} \mathbf{\varepsilon} \mathbf{B} \mathbf{a} \partial \Omega + | ||

\oint_{\Gamma_{\infty}} \mathbf{N^T} \alpha \mathbf{N} \mathbf{a} \partial \Gamma_{\infty} = | \oint_{\Gamma_{\infty}} \mathbf{N^T} \alpha \mathbf{N} \mathbf{a} \partial \Gamma_{\infty} = | ||

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

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

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

## 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):