Elastohydrodynamic lubrication for line and point contacts : asymptotic and numerical approaches Preface. Since the ground breaking numerical study by Petrusevich [1] and approximate analytical studies by Ertel and Grubin [2 3] of elastohydrodynamic lubrication (EHL) problems were published over sixty years these two approaches i.e. the direct numerical solution of EHL problems and Ertel like approximate analysis of EHL problems completely dominated the field of EHL research. There were a number of different numerical methods developed as well as some analytical variations of the Ertel method. However most studies of EHL problems were done numerically. Practically all these numerical methods work really well in cases when an EHL contact is lightly to moderately heavily loaded. At the same time all direct numerical methods applied to heavily loaded isothermal EHL problems suffer from solution instability which results in poor solution convergence and precision in the exit zone of a contact. With the transition from the numerical solution of two dimensional EHL problems (line contacts) to three dimensional EHL problems (point contacts) the difficulties just get exacerbated. Therefore the time has come to understand the roots of most difficulties in direct numerical approaches to solution of EHL problems and provide an effective remedy. The idea of most direct numerical methods is to take a numerical solver based on a particular numerical procedure (Newton Raphson method Maltilevel Maltigrid method Fast Fourier Transform method etc.) and apply it more or less uniformly to all points of a lubricated contact region to obtain a solution of an EHL problem without any regard to different physical mechanisms driving the lubrication phenomenon in a particular subregion of the lubricated contact