A finite element solver for Laplace's equation
We use finite elements when the size of the data is so large that its results prohibit dealing with finite differences. To illustrate this case, we would like to explore the numerical solution of the Laplace equation, subject to certain boundary conditions.
We will start by defining the computational domain and produce a mesh dividing this domain using triangles as local finite elements. This will be our starting point to solve this problem using finite elements, as we will be placing on the computational domain a piecewise continuous function, whose pieces are linear and supported on each of the triangles.
We start by calling the necessary modules to build the mesh (other modules will be called as they are required):
>>> import numpy >>> from numpy import linspace >>> import scipy >>> import matplotlib.pyplot as plt >>> from scipy.spatial import Delaunay
First we define the region:
>>>...
