|Illustration of the Finite element method, the computed solution. (Photo credit: Wikipedia)|
A simple finite element code in Julia for solving the 2D Poisson equation over the unit square is presented in this article. The code uses only Julia's standard library and thus does not have any external dependencies. It solves the partial differential equation u,xx + u,yy = -6 over the unit square with the Dirichlet boundary condition u = 1 + x^2 + 2y^2 on the sides of the unit square. The code can however be easily modified to study other instances of the Poisson equation. The unit square is discretized with linear triangular finite elements and the stiffness matrix and load vectors are calculated using a one-point quadrature rule.
Finite Element programming in Julia - CodeProject