Finite Difference and Elements code
Finite difference:
A simple finite difference application for solving hyperbolic equations of consevation laws.
Grid used: So far a equidistant Cartesian grid is generated with arbitraty amount of points in 1, 2 and 3 space dimension.
Type of equations: 1D Scalar conservation laws (planning to extend it to multi-dimensional systems).
Initial conditions implemented: Gaussian bell exp(-x^2), sin(x). and step function.
Test cases implemented: 1D inviscid Burgers' equation.
Finite Elements:
A polynomial basis function class was implemented including functions to multiply, integrate and differenciate polynomials. There is an initial implementation of 1-dimensional Legendre polynomial basis until order 4.
A class for the finite element grid was created based in three objects: the polynomial basis, a vector of cell objects, and a triangulation.