Studies on enhanced robust finite element schemes for viscoelastic flows

The target is to attain ever more efficient and robust finite element solvers and to construct software for realistic constitutive models. Algorithmic variations to achieve this include upwinding, discontinuity capturing,embedded recovery of gradients [j27] and residual-based stabilisation. A unifying theme is to permit the efficient, accurate and stable use of multiple relaxation times and consideration of three-dimensional or complex flows in viscoelastic modelling. Our more recent work on finite elements and recovery methods is summarised in the extensive article by Matallah et al. [j16]. This addresses various recovery and stress splitting schemes for viscoelastic flows. Recovery-based schemes are found to be stability enhancing, re higher elasticity number attenuation. 
The recovery aspect, and not the stress-splitting, is the key element responsible for this improvement, capturing improved stability through enhanced accuracy. This work is supported by EPSRC funding under the ROPA scheme.