Un An\'alisis Comparativo de los M\'etodos Mim\'eticos, Diferencias Finitas y Elementos Finitos para problemas Estacionarios

TL;DR

This paper compares mimetic finite differences, finite element, and finite difference methods for solving steady boundary value problems, analyzing their efficiency, convergence order, and computational cost in one-dimensional convection-diffusion equations.

Contribution

It provides a comparative analysis of three numerical methods focusing on their performance and convergence in steady-state convection-diffusion problems.

Findings

Mimetic methods show comparable convergence to finite elements.

Finite difference methods are computationally efficient.

All methods demonstrate expected convergence orders.

Abstract

Numerical methods: mimetic finite differences and finite elements, are analyzed from a numerical point of view. It seeks to conclude on the efficiency, order of convergence and computational cost of these methods. The analysis is done in boundary value problems one-dimensional (convection-diffusion equation at steady) with different variations in the gradient, diffusion coefficient and convective velocity. Key Words: Mimetics methods, Finite Element methods, Finite differences methods, Conservative methods, Convergence.