TY - JOUR T1 - Numerical Approximation of Viscoelastic Flows in an Elastic Medium JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 125 EP - 143 PY - 2015 DA - 2015/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/481.html KW - viscoelastic flow, elastic structure, finite elements. AB -

We study the numerical approximation of a flow problem governed by a viscoelastic model coupled with a one-dimensional elastic structure equation. A variational formulation for flow equations is developed based on the Arbitrary Lagrangian-Eulerian (ALE) method and stability of the time discretized system is investigated. For decoupled numerical algorithms we consider both an explicit scheme of the Leap-Frog type and a fully implicit scheme.