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Description:
In the present paper, we consider a specific class of non-autonomous wave equations on a smooth, bounded domain and their discretization in space by isoparametric finite elements and in time by the implicit Euler method. Building upon the work of Baker and Dougalis (1980), we prove maximum norm estimates for the semi discretization in space and the full discretization. The key tool is the gain of integrability coming from the inverse of the discretized differential operator. For this, we have to pay with time derivatives on the error in the $L^2$-norm which are reduced to estimates of the differentiated initial errors.