Convergence and error estimates for finite element solutions of elastohydrodynamic lubrication

Wu, S. David; Oden, J. Tinsley

doi:10.1016/0898-1221(87)90119-2

Cited by 3 publications

(1 citation statement)

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“…It is worth remarking that the theoretical properties of the solution to these equations are not well understood. One notable exception is the finite element analysis of Wu and Oden [41,42,43] who considered lightly loaded EHL cases. One theoretical issue, addressed by Stenger, for example [33,34], is that the film thickness H(x, y) is uniquely defined by the pressure P (x, y) via (3.3).…”

Section: Notationmentioning

confidence: 99%

Adaptive Timestepping for Elastohydrodynamic Lubrication Solvers

Goodyer¹,

Berzins²

2006

SIAM J. Sci. Comput.

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The application of variable-step time-integration techniques in a method of lines approach for the numerical solution of transient elastohydrodynamic lubrication calculations is described. Spatial discretization of the coupled integro-differential equations leads to a system of differential-algebraic equations in time. At each timestep a large system of nonlinear equations of 10 4-10 7 variables is solved by using multigrid methods and multilevel multi-integration. The application of temporal error control methods is considered with reference to both the differential-algebraic formulation of the system to be solved and the multigrid-based nonlinear equation solver to be used. The error control method used takes account of the magnitude of the spatial error present by using a local time error control based on the magnitude of this error. This approach is shown to be beneficial in reducing the computational work required. Experimental results on a variety of lubrication problems, including a challenging rough surface problem, are used to display the effectiveness of the methods.

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