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The focus of the present work is the (theoretical) approximation of asolution of the p(x)-Poisson equation. To devise an iterative solver withguaranteed convergence, we will consider a relaxation of the original problemin terms of a truncation of the nonlinearity from below and from above by usinga pair of positive cut-off parameters. We will then verify that, for any suchpair, a damped Ka\v{c}anov scheme generates a sequence converging to a solutionof the relaxed equation. Subsequently, it will be shown that the solutions ofthe relaxed problems converge to the solution of the original problem in thediscrete setting. Finally, the discrete solutions of the unrelaxed problemconverge to the continuous solution. Our work will finally be rounded up withsome numerical experiments that underline the analytical findings.

A damped Ka\v{c}anov scheme for the numerical solution of a relaxed p(x)-Poisson equation