We study a~priori estimates for the Dirichlet problem of the
p(⋅)-Laplacian, −div(∣∇v∣p(⋅)−2∇v)=f.
We show that the gradients of the finite element approximation with zero
boundary data converges with rate O(hα) if the exponent p is
α-H\"{o}lder continuous. The error of the gradients is measured in the
so-called quasi-norm, i.e. we measure the L2-error of ∣∇v∣2p−2∇v