Energy stable and accurate coupling of finite element methods and finite difference methods

TL;DR

This paper presents a hybrid coupling method combining finite element and finite difference techniques to efficiently and accurately simulate complex geometries while ensuring stability and energy conservation.

Contribution

A novel nonconforming multiblock coupling approach that maintains stability, accuracy, and energy conservation with minimal modifications to existing schemes.

Findings

Stable coupling demonstrated on scalar conservation laws

High-order accuracy achieved in complex geometries

Energy conservation maintained in simulations

Abstract

We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries are present. The proposed coupling technique requires minimal changes in the existing schemes while maintaining strict stability, accuracy, and energy conservation. Results are demonstrated on linear and nonlinear scalar conservation laws in two spatial dimensions.