Local discontinuous Galerkin approximation of non-Fickian diffusion model in viscoelastic polymers

Abstract

In this paper, we investigate a fully discrete local discontinuous Galerkin approximation of a non-linear non-Fickian diffusion model in viscoelastic polymers. For the spatial discretization, we adopt local discontinuous Galerkin finite element method and for the time discretization we use backward Euler method. We derive the stability estimate and a priori error estimate for the discrete scheme. Numerical examples are given to verify the theoretical findings.

Keywords:

• local discontinuous Galerkin method
• non-Fickian diffusion
• error estimates

AMS Subject Classifications:

• 65N30
• 65N15
• 65N12

Acknowledgments

The authors would like to thank the editors and referees for their valuable suggestions which greatly improved this paper.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11301311], [grant number 11171193]; Young Scientists Fund of Shandong Province [grant number 2008BS01008] and [grant number BS2011NJ016].