# Continuous time integration for changing type systems

## TL;DR

This paper introduces a continuous time integration method for systems with evolving types, proving optimal convergence and demonstrating its effectiveness through numerical examples.

## Contribution

It develops a variational time integration approach using continuous Galerkin Petrov methods for changing type systems, with proven optimal error convergence.

## Key findings

- Proven optimal-order convergence of the method.
- Numerical examples demonstrating the method's effectiveness.
- Theoretical analysis of error bounds.

## Abstract

We consider variational time integration using continuous Galerkin Petrov methods applied to evolutionary systems of changing type. We prove optimal-order convergence of the error in a cGP-like norm and conclude the paper with some numerical examples and conclusions.