  We consider the numerical approximation of variational problems with
orthotropic growth, that is those where the integrand depends strongly on the
coordinate directions with possibly different growth in each direction. Under
realistic regularity assumptions we derive optimal error estimates. These
estimates depend on the existence of an orthotropically stable interpolation
operator. Over certain meshes we construct an orthotropically stable
interpolant that is also a projection. Numerical experiments illustrate and
explore the limits of our theory.
