Equal-Order Stabilized Finite Element Approximation of the p-Stokes Equations on Anisotropic Cartesian Meshes
2020 ◽
Vol 20
(1)
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pp. 1-25
Keyword(s):
A Priori
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AbstractThe 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 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.
2006 ◽
Vol 16
(02)
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pp. 233-263
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2006 ◽
Vol 44
(5)
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pp. 1903-1920
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1995 ◽
Vol 29
(3)
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pp. 367-389
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Keyword(s):
2004 ◽
Vol 14
(04)
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pp. 603-618
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1991 ◽
Vol 57
(195)
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pp. 123-123
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