Finite element approximation of the p(·)-laplacian

Abstract. We study a priori estimates for the p(·)-Laplace Dirichlet problem, −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-Hölder continuous. The error of the gradients is measured in the so-called quasi-norm, i.e. we measure the L2-error of |∇v | p−22 ∇v. variable exponents, convergence analysis, a priori estimates, finite element method, generalized Lebesgue and Sobolev spaces MSC 2010: 65N15, 65N30, 65D05, 35J60, 46E3