TY - JOUR AU - Lugo Jiménez, Abdul Abner AU - Mata Díaz, Guelvis Enrique AU - Ruiz, Bladismir PY - 2021/07/29 Y2 - 2024/03/29 TI - A comparative analysis of methods: mimetics, finite differences and finite elements for 1-dimensional stationary problems JF - Selecciones Matemáticas JA - Sel.Mat. VL - 8 IS - 01 SE - DO - 10.17268/sel.mat.2021.01.01 UR - https://revistas.unitru.edu.pe/index.php/SSMM/article/view/3696 SP - 1 - 11 AB - <p>Numerical methods are useful for solving differential equations that model physical problems, for example,&nbsp;heat transfer, fluid dynamics, wave propagation, among others; especially when these cannot be solved by&nbsp;means of exact analysis techniques, since such problems present complex geometries, boundary or initial&nbsp;conditions, or involve non-linear differential equations. Currently, the number of problems that are modeled&nbsp;with partial differential equations are diverse and these must be addressed numerically, so that the results&nbsp;obtained are more in line with reality. In this work, a comparison of the classical numerical methods such&nbsp;as: the finite difference method (FDM) and the finite element method (FEM), with a modern technique of&nbsp;discretization called the mimetic method (MIM), or mimetic finite difference method or compatible method,&nbsp;is approached. With this comparison we try to conclude about the efficiency, order of convergence of these&nbsp;methods. Our analysis is based on a model problem with a one-dimensional boundary value, that is, we&nbsp;will study convection-diffusion equations in a stationary regime, with different variations in the gradient,&nbsp;diffusive coefficient and convective velocity.</p> ER -