Numerical methods for evolutionary problems in partial differential equations and control - Guillermo Villa Martínez; Carlos Alberto Ramírez Vanegas; Oscar Danilo Montoya Giraldo (Statistics, Optimization & Information Computing, 2025)
In this paper we implement the finite element method for parabolic problems with dominant transport terms. The formulation of the linear system of equations coming from a partial differential equation takes its form from the weakening of the problem. Several numerical experiments are performed to know the convergence of the solution and an error analysis in a Sobolev space for linear functions is implemented.