An optimal convergence analysis of the hybrid Raviart-Thomas mixed discontinuous Galerkin method for the Helmholtz equation

TL;DR

This paper introduces an optimal convergence analysis for a hybrid Raviart-Thomas mixed discontinuous Galerkin method applied to the Helmholtz equation, demonstrating its stability and accuracy independent of wavenumber.

Contribution

The paper develops a new energy norm and proves the existence, uniqueness, and optimal convergence of the HRTMDG method for the Helmholtz equation.

Findings

Establishes the existence and uniqueness of the HRTMDG method.

Proves optimal $L^2$-norm convergence independent of wavenumber.

Provides a new energy norm for stability analysis.

Abstract

The hybrid Raviart-Thomas mixed discontinuous Galerkin (HRTMDG) method is proposed for solving the Helmholtz equation. With a new energy norm, we establish the existence and uniqueness of the HRTMDG method, and give its convergence analysis. The corresponding error estimate shows that the HRTMDG method has an optimal $L^2$-norm convergence accuracy which is independent of wavenumber.