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

Antonio Márquez and Salim Meddahi

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. Finally, we discuss full discretization strategies for both Galerkin methods.

MSC 2010: 65N30; 65M12; 65M15; 74H15

* This research was supported by Spain’s Ministry of Economy Project MTM2017-87162-P.


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Published Online: 2021-07-03

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