# Scattering-Passive Structure-Preserving Finite Element Method for the Boundary Controlled Transport Equation with a Moving Mesh

arXiv: https://arxiv.org/abs/2402.01232 · HTML: https://mlsanity.com/paper/2402.01232/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Feb 2024.

## Built on by (most cited first, 1 of 1)

- [Towards a Design Guideline for RPA Evaluation: A Survey of Large Language Model-Based Role-Playing Agents](https://mlsanity.com/paper/2502.13012/) (2025)

## Abstract (arXiv)

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.