An Evaluation of Finite Difference and Finite Element Methods for the Solution of the Reynolds Equation

A comparative study is made of various finite difference and finite element solutions of the Reynolds equation for the steady, isoviscous, incompressible hydrodynamic lubrication problem. Numerical solutions are obtained for both one- and two-dimensional slider bearings, and the predicted load capacity is evaluated against that of the corresponding exact analytical solution. Two finite difference schemes of nominal second-and fourth-order accuracy are employed. Linear, quadratic, and cubic elements are used in the finite element solutions. The different solution methods are evaluated in terms of accuracy, computational complexities and cost.