Superconductivity was discovered in 1911 and since then it has become indispensable in a wide range of fields. It is often accompanied by strong magnetic fields which can do away with the superconducting properties of the material. This process is described by the Ginzburg-Landau theory of superconductivity. In this report, this theory is discussed at length. The result is a system of two coupled, time-dependent partial differential equations that can be solved using numerical methods. A nite element method is constructed using standard Lagrangian and curl-conforming Nedelec elements. Numerical simulations were performed with Lagrangian and Nedelec elements in COMSOL and MATLAB respectively. Using Lagrangian elements delivers flawed results. Using Nedelec elements should improve these results but so far only parts of the problem have successfully been solved using these elements.