An abradable coating system (2-8) for a turbine or a compressor is proposed has at least one layer of woven or non-woven tissue (15) or foam made of: ceramic, glass, glass-ceramic, ceramic-metal composite and combinations thereof. A free-standing preformed element (18) has at least one layer of such a woven or non-woven tissue or foam is filled with fillers and/or binder. A method prepares such a system. Finally, a method for the repair of an abradable coating portion of a turbine or the compressor component (9) includes in a first optional step that the damaged portion is at least partly removed and/or cleaned and/or surface treated, and in a second step at least one free-standing preformed abradable coating element (18) or a complete abradable coating system is attached to the component (9), preferably by using a matrix, wherein for example only a center part (2) or a fraction of a center part (2) is replaced.