A Note On A Norm-Preserving Continuous Galerkin Time Stepping Scheme

TL;DR

This paper introduces a variable-order continuous Galerkin time stepping scheme designed to preserve norms in dynamical systems and provides an a posteriori error estimate for the maximum norm.

Contribution

It develops a novel norm-preserving continuous Galerkin method with an a posteriori error estimate tailored for dynamical systems.

Findings

The scheme effectively preserves the system's norm.

An a posteriori $L^ abla$-error estimate is established.

The method is suitable for dynamical systems requiring norm preservation.

Abstract

In this note we shall devise a variable-order continuous Galerkin time stepping method which is especially geared towards norm-preserving dynamical systems. In addition, we will provide an a posteriori estimate for the $L^\infty$-error.