An economical finite element approximation of generalized Newtonian flows Original Research Article

We consider an economical bilinear rectangular mixed finite element scheme on regular mesh for generalized Newtonian flows, where the viscosity obeys a Carreau type law for a pseudo-plastic. The key issue in the scheme is that the two components of the velocity and the pressure are defined on different meshes. Optimal error bounds for both the velocity and pressure are obtained by proving a discrete Babus̆ka–Brezzi inf–sup condition on the regular quadrangulation. Finally, we perform some numerical experiments, including an example in a unit square with exact solutions, a backward-facing step and a four-to-one abrupt contraction generalized Newtonian flows. Numerical experiments confirm our error bounds.