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.
Funding statement: This research was supported by Spain’s Ministry of Economy Project MTM2017-87162-P.
References
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- An energy, momentum, and angular momentum conserving scheme for a regularization model of incompressible flow
- Numerical simulation for European and American option of risks in climate change of Three Gorges Reservoir Area
- Mixed-hybrid and mixed-discontinuous Galerkin methods for linear dynamical elastic–viscoelastic composite structures
- POD-Galerkin model order reduction for parametrized nonlinear time-dependent optimal flow control: an application to shallow water equations
Artikel in diesem Heft
- Frontmatter
- An energy, momentum, and angular momentum conserving scheme for a regularization model of incompressible flow
- Numerical simulation for European and American option of risks in climate change of Three Gorges Reservoir Area
- Mixed-hybrid and mixed-discontinuous Galerkin methods for linear dynamical elastic–viscoelastic composite structures
- POD-Galerkin model order reduction for parametrized nonlinear time-dependent optimal flow control: an application to shallow water equations