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We revise the finite element formulation for Lagrange, Raviart- Thomas, andTaylor-Hood finite element spaces. We solve Laplace equation in first andsecond order formulation, and compare the solutions obtained with Lagrange andRaviart-Thomas finite element spaces by changing the order of the shapefunctions and the refinement level of the mesh. Finally, we solve Navier-Stokesequations in a two dimensional domain, where the solution is a steady state,and in a three dimensional domain, where the system presents a turbulentbehaviour. All numerical experiments are computed using MFEM library, which isalso studied.

Numerical approximation of partial differential equations with MFEM library