Discontinuous Galerkin Infrastructure For the finite element toolbox Ferrite.jl

This project aims to implement the necessary infrastructure for the Discontinuous Galerkin method in the finite element toolbox Ferrite.jl. This will include writing examples, documentation, and tests. DG method is a FEM like the continuous Galerkin (CG) method where the test functions are chosen to be the same as the trial functions. However, DG elements do not share degrees of freedom (DoF) at common nodes, introducing extra DoF and adding the process of choosing coupling between elements through numerical fluxes. The main deliverables are: • Methods to integrate on inner faces. • Extend the methods to integrate over subfaces. • Sparsity pattern methods for DG. • Implement infrastructure for handling boundary conditions for DG approximations. • 1-D, 2-D, and 3-D steady heat equation using DG example. • Testing and documentation for all implemented methods.