Finite Element Mesh Adjusted to Singularities Applied to Axisymmetric and Plane Flow

Pavel Burda (), Jaroslav Novotný (), Bedřich Sousedík () and Jakub Šístek ()
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Pavel Burda: Czech Univ. Technology, Department of Mathematics, Faculty of Mechanical Engineering
Jaroslav Novotný: Institute of Thermomechanics AS CR
Bedřich Sousedík: Czech University of Technology, Department of Mathematics, Faculty of Civil Engineering
Jakub Šístek: Czech Univ. Technology, Department of Mathematics, Faculty of Mechanical Engineering

A chapter in Numerical Mathematics and Advanced Applications, 2004, pp 186-195 from Springer

Abstract: Summary We consider the Navier-Stokes equations for incompressible flow in axisymmetric tubes with abrupt changes of diameter. This paper is based on results for the asymptotics of the solution in the vicinity of nonconvex internal angles where the velocities possess an expansion u(ρ, ϑ) = ρ γ ϕ(ϑ) + …, where ρ, ϑ are local spherical coordinates. Problems with corners, edges, etc. are often successfully solved by the finite element method using an adaptive strategy usually based on a posteriori error estimates. In our paper we suggest an alternative approach for the mesh refinement near the corners, which makes use of the above expansion. It gives very precise results in a cheap way. We give numerical results and show the pros and cons of this approach.

Keywords: Finite Element Method; Mesh Refinement; Stokes Flow; Stokes Problem; Posteriori Error Estimate (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18775-9_16

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DOI: 10.1007/978-3-642-18775-9_16

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