Equal-Order Stabilized Finite Element Approximation of the p-Stokes Equations on Anisotropic Cartesian Meshes

Josefin Ahlkrona, Malte Braack
2019 Computational Methods in Applied Mathematics  
The p-Stokes equations with power-law exponent {p\in(1,2)} describes non-Newtonian, shear-thinning, incompressible flow. In many industrial applications and natural settings, shear-thinning flow takes place in very thin domains. To account for such anisotropic domains in simulations, we here study an equal-order bi-linear anisotropic finite element discretization of the p-Stokes equations, and extend a non-linear Local Projection Stabilization to anisotropic meshes. We prove an a priori
more » ... and illustrate the results with two numerical examples, one confirming the rate of convergence predicted by the a-priori analysis, and one showing the advantages of an anisotropic stabilization compared to an isotropic one.
doi:10.1515/cmam-2018-0260 fatcat:6cdk7reuanf3znj3aqjzfza4ge