We study a~priori estimates for the Dirichlet problem of the \(p(\cdot)\)-Laplacian, \[-\mathrm{div}(|\nabla v|^{p(\cdot)-2} \nabla v) = f. \] We show that the gradients of the finite element approximation with zero boundary data converges with rate \(O(h^\alpha)\) if the exponent \(p\) is \(\alpha\)-H\"{o}lder continuous. The error of the gradient...

Finite element approximation of the \(p(\cdot)\)-Laplacian