# Solving PDEs#

Here we show how the *discretize* package can be used to solve partial differential
equations (PDE) numerically by employing the finite volume method. To solve a PDE
numerically we must complete the following steps:

Formulate the problem; e.g. the PDE and its boundary conditions

Apply the weak formulation by taking the inner product of each PDE with a test function

Formulate a discrete set of equations for the inner products according to the finite volume method

Use the discrete set of equations to solve for the unknown variable numerically

Gauss' Law of Electrostatics

Advection-Diffusion Equation