Numerical methods for changing type systems

TL;DR

This paper introduces a numerical method for solving PDEs with changing types, utilizing a unified solution theory and a discontinuous Galerkin approach in space-time with weighted spaces.

Contribution

The paper develops a novel numerical method based on Picard's unified solution theory, tailored for PDEs with changing types, using a discontinuous Galerkin framework.

Findings

Effective for PDEs with changing types

Utilizes a unified solution theory by Picard

Employs a discontinuous Galerkin approach in space-time

Abstract

In this note we develop a numerical method for partial differential equations with changing type. Our method is based on a unified solution theory found by Rainer Picard for several linear equations from mathematical physics. Parallel to the solution theory already developed, we frame our numerical method in a discontinuous Galerkin approach in space-time with certain exponentially weighted spaces.