Symmetric mixed discontinuous Galerkin methods for linear viscoelasticity

TL;DR

This paper introduces symmetric mixed discontinuous Galerkin methods for linear viscoelasticity, combining high-order spatial discretization with a Newmark time scheme, and provides stability analysis and numerical validation.

Contribution

It develops and analyzes novel symmetric mixed DG methods for viscoelasticity, ensuring stability and convergence with arbitrary-order spatial discretization.

Findings

Methods are stable and convergent.

Numerical simulations confirm theoretical results.

Applicable in 2D and 3D scenarios.

Abstract

We propose and rigorously analyse semi- and fully discrete discontinuous Galerkin methods for an initial and boundary value problem describing inertial viscoelasticity in terms of elastic and viscoelastic stress components, and with mixed boundary conditions. The arbitrary-order spatial discretisation imposes strongly the symmetry of the stress tensor, and it is combined with a Newmark trapezoidal rule as time-advancing scheme. We establish stability and convergence properties, and the theoretical findings are further confirmed via illustrative numerical simulations in 2D and 3D.