A tent pitching scheme motivated by Friedrichs theory

TL;DR

This paper introduces a tent pitching finite element scheme inspired by Friedrichs theory, designed to handle advective problems with weak boundary trace continuity, and demonstrates its effectiveness on a wave propagation model.

Contribution

It develops a novel space-time finite element method conforming to a weak boundary trace continuity property derived from Friedrichs systems.

Findings

Numerical results validate the scheme's effectiveness.

The method accurately models wave propagation.

The scheme handles boundary trace continuity issues.

Abstract

Certain Friedrichs systems can be posed on Hilbert spaces normed with a graph norm. Functions in such spaces arising from advective problems are found to have traces with a weak continuity property at points where the inflow and outflow boundaries meet. Motivated by this continuity property, an explicit space-time finite element scheme of the tent pitching type, with spaces that conform to the continuity property, is designed. Numerical results for a model one-dimensional wave propagation problem are presented.