Abstract A fully coupled high order discontinuous Galerkin (DG) solver for viscoelastic Oldroyd B fluid flow problems is presented. Contrary to known methods combining DG the discretization of convective terms material model with standard finite element (FEM) and using elastic viscous stress splitting (EVSS) its derivatives, a local (LDG) formulation first described hyperbolic convection‐diffus...

Many small organisms self-propel in viscous fluids using travelling wave-like deformations of their bodies or appendages. Examples include small nematodes moving through soil using whole-body undulations or spermatozoa swimming through mucus using flagellar waves. When self-propulsion occurs in a non-Newtonian fluid, one fundamental question is whether locomotion will occur faster or slower tha...

In this article we consider the numerical approximation to the time dependent viscoelasticity equations with an Oldroyd B constitutive equation. The approximation is stabilized by using a SUPG approximation for the constitutive equation. We analyse both the semi-discrete and fully discrete numerical approximations. For both discretizations we prove the existence of, and derive a priori error es...