We consider the problem of estimating a high-dimensional additive mixed model for longitudinal data using sparse methods. In this problem, multiple measurements are made on the same subject across time, and then the different sources of variability (intra- and inter-subject variability) and correlation within subjects have to be considered. Also, the relationships between explanatory variables and the outcome are possibly non linear. In addition, the number of explanatory variables could be larger than the sample size but only a small set of explanatory variables contribute to the response. Several computational approaches for high-dimensional additive modelling for independent data have been developed in the literature. Recently, Amato and colleagues (Stat Methods Appl 2016; s10260-016-0357-8) conducted a comprehensive review of these methods. Efficient regularized estimation procedures for variable selection in nonparametric additive models use basis function approximations. The authors also proposed a reformulation of the estimation problem in terms of group Lasso that allows deducing convergence and asymptotic optimality properties. Only a few works have developed suggestions to analyse high-dimensional longitudinal data using Lasso-type methods in additive mixed model. The resulting estimator depends only on a relatively small number of basis functions, however variable selection is not directly encouraged. In this study we explore the extension of the group Lasso penalty to additive mixed effects models. We discuss computational aspects, including a comparison of group Lasso algorithms implemented through publicly available R codes, the estimation of optimal regularization parameter and linkages between mean and covariance parameter estimation algorithms. We illustrate the interest of such approaches in the analysis of a twenty - year longitudinal study of training practices of elite athletes.