Numerical approximation of partial differential equations with MFEM library
Numerical Analysis
2022-12-01 v1 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2211.16612,
title = {Numerical approximation of partial differential equations with MFEM library},
author = {Felipe Cruz},
journal= {arXiv preprint arXiv:2211.16612},
year = {2022}
}
Comments
Undergrad degree work. 65 pages. arXiv admin note: text overlap with arXiv:2105.03002