# An improved high order finite difference method for non-conforming grid interfaces for the wave equation

## TL;DR

This paper develops a stable, high-order finite difference method for the wave equation on non-conforming grids, extending stability proofs to sixth order accuracy through new penalty terms, and demonstrates improved stability and accuracy.

## Contribution

It introduces new penalty terms that enable stability of sixth order schemes on non-conforming interfaces, overcoming previous limitations.

## Key findings

- Sixth order scheme is now provably stable.
- Numerical experiments confirm improved accuracy.
- Enhanced stability for high-order methods on complex grids.

## Abstract

This paper presents an extension of a recently developed high order finite difference method for the wave equation on a grid with non-conforming interfaces. The stability proof of the existing methods relies on the interpolation operators being norm-contracting, which is satisfied by the second and fourth order operators, but not by the sixth order operator. We construct new penalty terms to impose interface conditions such that the stability proof does not require the norm-contracting condition. As a consequence, the sixth order accurate scheme is also provably stable. Numerical experiments demonstrate the improved stability and accuracy property.