DeepAI AI Chat
Log In Sign Up

Analysis of a mixed discontinuous Galerkin method for the time-harmonic Maxwell equations with minimal smoothness requirements

09/14/2020
by   Kaifang Liu, et al.
0

An error analysis of a mixed discontinuous Galerkin (DG) method with Brezzi numerical flux for the time-harmonic Maxwell equations with minimal smoothness requirements is presented. The key difficulty in the error analysis for the DG method is that the tangential or normal trace of the exact solution is not well-defined on the mesh faces of the computational mesh. We overcome this difficulty by two steps. First, we employ a lifting operator to replace the integrals of the tangential/normal traces on mesh faces by volume integrals. Second, optimal convergence rates are proven by using smoothed interpolations that are well-defined for merely integrable functions. As a byproduct of our analysis, an explicit and easily computable stabilization parameter is given.

READ FULL TEXT

page 1

page 2

page 3

page 4

03/11/2019

A hybridizable discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations

In this paper, we aim to develop a hybridizable discontinuous Galerkin (...
12/21/2020

A p-robust polygonal discontinuous Galerkin method with minus one stabilization

We introduce a new stabilization for discontinuous Galerkin methods for ...
04/16/2021

Unified Analysis of Discontinuous Galerkin Methods for Frictional Contact Problem with normal compliance

In this article, a reliable and efficient a posteriori error estimator o...
05/31/2023

A hybridizable discontinuous Galerkin method for magnetic advection-diffusion problems

We propose and analyze a hybridizable discontinuous Galerkin (HDG) metho...
04/21/2022

Convergence analysis of a Local Discontinuous Galerkin approximation for nonlinear systems with Orlicz-structure

In this paper, we investigate a Local Discontinuous Galerkin (LDG) appro...
06/06/2023

Convergence analysis of nonconform H(div)-finite elements for the damped time-harmonic Galbrun's equation

We consider the damped time-harmonic Galbrun's equation, which is used t...
11/14/2022

p-adaptive algorithms in Discontinuous Galerkin solutions to the time-domain Maxwell's equations

The Discontinuous Galerkin time-domain method is well suited for adaptiv...