The modeling of friction stir welding (FSW) is challenging as severe plastic deformation is present. This is in particular the case as typical finite element methods are employed. In this study we use a meshfree technique to model the material flow during the FSW process. We employ the Element-Free Galerkin method (EFG) as approximation method. A mortar contact is used to account for the stirring effect and heat generation from the frictional contact. A two-way adaptive method (rh-adaptive) during the coupled thermomechanical process is used to overcome potential numerical problems arising from the extensive mesh distortion and material deformation. This means, the mesh is globally refined with perusing an anisotropic tetrahedral mesh (h-adaptive). At the same time, a completely new mesh is built based on the old mesh (r-adaptive). Finally, we perform the simulation method on an aluminum sheet with a cylindrical tool to exemplarily show the applicability of the adaptive Element-Free Galerkin method. In future work, the obtainable deformation and temperature history from the thermomechanical simulation will be used to predict the final micro-structure after the welding process.