A space-time discontinuous Galerkin method for convection and diffusion in injection moulding

In this article, we investigate a space-time finite element method for solving the convection-diffusion-reaction equation. This method is based on a discontinuous Galerkin technique using low order elements in space and high order elements in time. The suggested method is applied to solve the transport equation and the heat equation in 3D mold filling. An original mixed approach is investigated to solve the steady diffusion equation. The proposed numerical scheme is validated through analytical examples, then applied to 3D industrial simulations in injection molding process. Several examples show that the computed solutions are stable, robust and fast.