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

Ahlkrona, Josefin and Braack, Malte (2019) Equal-Order Stabilized Finite Element Approximation of the p-Stokes Equations on Anisotropic Cartesian Meshes. Computational Methods in Applied Mathematics . DOI 10.1515/cmam-2018-0260.

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Abstract

The p-Stokes equations with power-law exponent
p∈(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 estimate 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.

Document Type: Article
Keywords: Anisotropic Meshes; Finite Element Method; Shear-Thinning; Local Projection Stabilization
Research affiliation: Kiel University > Kiel Marine Science
OceanRep > The Future Ocean - Cluster of Excellence
Kiel University
Refereed: Yes
Open Access Journal?: No
DOI etc.: 10.1515/cmam-2018-0260
ISSN: 1609-4840
Projects: Future Ocean
Date Deposited: 01 Aug 2019 12:31
Last Modified: 02 Jan 2020 12:24
URI: http://oceanrep.geomar.de/id/eprint/47322

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