2024/02/02 by Jesus-Pablo Toledo-Zucco, Toledo-Zucco, Jesus-Pablo, Denis Matignon +3 · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Differential Equations and Numerical Methods #FOS: Electrical engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2402.01232
openalex publication_date 2024/02/02 · openalex created_date 2024/02/06 · openalex updated_date 2026/07/28
A structure-preserving Finite Element Method (FEM) for the transport equation in one- and two-dimensional domains is presented. This Distributed Parameter System (DPS) has non-collocated boundary control and observation, and reveals a scattering-energy preserving structure. We show that the discretized model preserves the aforementioned structure from the original infinite-dimensional system. Moreover, we analyse the case of moving meshes for the one-dimensional case. The moving mesh requires less states than the fixed one to produce solutions with a comparable accuracy, and it can also reduce the overshoot and oscillations of Gibbs phenomenon produced when using the FEM. Numerical simulations are provided for the case of a one-dimensional transport equation with fixed and moving meshes.