Mixed-hybrid and mixed-discontinuous Galerkin methods for linear dynamical elastic-viscoelastic composite structures

TL;DR

This paper develops and analyzes mixed-hybrid and mixed-discontinuous Galerkin methods for efficiently solving linear elastic-viscoelastic composite structures, ensuring stability and optimal error bounds.

Contribution

It introduces a stress-based formulation for Zener's model and provides a comprehensive analysis of discretization methods with proven error estimates.

Findings

Energy estimates guarantee well-posedness.

Optimal error bounds for discretizations.

Effective handling of heterogeneous materials.

Abstract

We introduce and analyze a stress-based formulation for Zener's model in linear viscoelasticity. The method is aimed to tackle efficiently heterogeneous materials that admit purely elastic and viscoelastic parts in their composition. We write the mixed variational formulation of the problem in terms of a class of tensorial wave equation and obtain an energy estimate that guaranties the well-posedness of the problem through a standard Galerkin procedure. We propose and analyze mixed continuous and discontinuous Galerkin space discretizations of the problem and derive optimal error bounds for each semidiscrete solution in the corresponding energy norm.