This paper addresses the development of efficient numerical solvers fo
r EHL problems from a rather fundamental point of view. A work-accurac
y exchange criterion is derived, that can be interpreted as setting a
limit to the price paid in terms of computing time for a solution of a
given accuracy. The criterion can serve as a guideline when reviewing
or selecting a numerical solver and a discretization. Earlier develop
ed multilevel solvers for the EHL line and circular contact problem ar
e tested against this criterion. This test shows that, to satisfy the
criterion a second-order accurate solver is needed for the point conta
ct problem whereas the solver developed earlier used a first-order dis
cretization. This situation arises more often in numerical analysis, i
.e., a higher order discretization is desired when a lower order solve
r already exists. It is explained how in such a case the multigrid met
hodology provides an easy and straightforward way to obtain the desire
d higher order of approximation. This higher order is obtained at almo
st negligible extra work and without loss of stability. The approach w
as tested out by raising an existing first order multilevel solver for
the EHL line contact problem to second order. Subsequently, it was us
ed to obtain a second-order solver for the EHL circular contact proble
m. Results for both the line and circular contact problem are presente
d.