论文标题
使用MFEM库的部分微分方程的数值近似
Numerical approximation of partial differential equations with MFEM library
论文作者
论文摘要
我们修改了拉格朗日，raviart-thomas和泰勒 - 霍德有限元元素空间的有限元公式。我们以一阶和二阶公式求解拉普拉斯方程，并通过更改形状函数的顺序和网格的细化水平来比较与拉格朗日和lagiart-thomas有限元元素空间获得的解决方案。最后，我们在二维结构域中求解Navier-Stokes方程，该方程是稳态的，在三维域中，系统呈现了湍流行为。所有数值实验均使用MFEM库计算，该库也经过研究。
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.
