QLunch: Learning how to solve PDEs via the FEM.

Speaker: Anton Samojlow from QMATH

Learning how to solve PDEs via the FEM.

The finite element method (FEM) is a numerical method to solve boundary value problems for partial differential equations (PDEs). I give a short introduction into the basics of the FEM and explain how to use it - without requiring any prior knowledge in numerical analysis (since I do not have any). The guiding example will be the Thomas-Fermi PDE for a homonuclear diatomic system. We in particular explain how to use the goal-oriented adaptation provided by the FEniCS platform to compute the dissociation energy in Thomas-Fermi theory. Last, we compare the obtained values to those from Hartree-Fock theory.