A fuel-cell assembly has a plurality of unit cells, each of the unit cells comprising an anode, an electrolyte, a cathode, and a current collector. The fuel-cell assembly has a plurality of electrical interconnection elements, at least one electrical interconnection element being connected respectively to each anode, to each cathode, and to each current collector of the unit cells. The unit cells are arranged in a stack and are mechanically supported by electrical interconnection elements such that each of the unit cells of the stack has at least one edge free to move relative to the electrical interconnection elements.