We revise the finite element formulation for Lagrange, Raviart- Thomas, and Taylor-Hood finite element spaces. We solve Laplace equation in first and second order formulation, and compare the solutions obtained with Lagrange and Raviart-Thomas finite element spaces by changing the order of the shape functions and the refinement level of the mesh. Finally, we solve Navier-Stokes equations in a two dimensional domain, where the solution is a steady state, and in a three dimensional domain, where the system presents a turbulent behaviour. All numerical experiments are computed using MFEM library, which is also studied.

翻译：我们修改 Lagrange、 Raviart-Thomas 和 Taylor-Hood 的有限元素空间的有限元素配方。 我们在第一和第二顺序配方中解决 Laplace 方程式,并通过改变形状函数的顺序和网状的精细水平来比较 Lagrange 和 Raviart-Thomas 的有限元素空间的解决方案。 最后, 我们用两个维域解决了Navier-Stokes 方程式, 其解决方案处于稳定状态, 并在三维域中解决了这个系统呈现动荡行为的方程式。 所有数字实验都使用MFEM 图书馆进行计算, 该图书馆也正在研究中 。