We propose and analyze in this article a finite element approximation, based on a penalty formulation, to a quasi-static unilateral contact problem between two thermoviscoelastic beams. An error bound is given and some numerical experiments discussed. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
domingo, 24 de enero de 2010
Numerical analysis of a contact problem between two thermoviscoelastic beams
We propose and analyze in this article a finite element approximation, based on a penalty formulation, to a quasi-static unilateral contact problem between two thermoviscoelastic beams. An error bound is given and some numerical experiments discussed. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
Partition of Unity Refinement for local approximation
In this article, we propose a Partition of Unity Refinement (PUR) method to improve the local approximations of elliptic boundary value problems in regions of interest. The PUR method only needs to refine the local meshes and hanging nodes generate no difficulty. The mesh qualities such as uniformity or quasi-uniformity are kept. The advantages of the PUR include its effectiveness and relatively easy implementation. In this article, we present the basic ideas and implementation of the PUR method on triangular meshes. Numerical results for elliptic Dirichlet boundary value problem on an L-shaped domain are shown to demonstrate the effectiveness of the proposed method. The extensions of the PUR method to multilevel and higher dimension are straightforward. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
A new approach for solving Stokes systems arising from a distributive relaxation method
The distributed relaxation method for the Stokes problem has been advertised as an adequate change of variables that leads to a lower triangular system with Laplace operators on the main diagonal for which multigrid methods are very efficient. We show that under high regularity of the Laplacian, the transformed system admits almost block-lower triangular form. We analyze the distributed relaxation method and compare it with other iterative methods for solving the Stokes system. We also present numerical experiments illustrating the effectiveness of the transformation which is well established for certain finite difference discretizations of Stokes problems. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
Numerical simulation of generalized Newtonian blood flow past a couple of irregular arterial stenoses
This paper looked at the numerical investigations of the generalized Newtonian blood flow through a couple of irregular arterial stenoses. The flow is treated to be axisymmetric, with an outline of the stenoses obtained from a three dimensional casting of a mild stenosed artery, so that the flow effectively becomes two-dimensional. The Marker and Cell (MAC) method is developed for the governing unsteady generalized Newtonian equations in staggered grid for viscous incompressible flow in the cylindrical polar co-ordinates system. The derived pressure-Poisson equation was solved using Successive-Over-Relaxation (S.O.R.) method and the pressure-velocity correction formulae have been derived. Computations are performed for the pressure drop, the wall shear stress distribution and the separation region. The presented computations show that in comparison to the corresponding Newtonian model the generalized Newtonian fluid experiences higher pressure drop, lower peak wall shear stress and smaller separation region. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010
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