In this paper, we develop two finite element formulations for the Laplace problem and find the way in which they are equivalent. Then we compare the solutions obtained by both formulations, by changing the order of the shape functions and the refinement level of the mesh (star with rhomboidal elements). And, we will give an overview of MFEM library from the LLNL (Lawrence Livermore National Laboratory), as it is the library used to obtain the solutions.