We propose a novel Eulerian algorithm to compute the changes of a glacier geometry for given mass balances. The surface of a glacier is obtained by solving a transport equation for the volume of fluid (VOF). The surface mass balance is taken into account by adding an interfacial term in the transport equation. An unstructured mesh with standard stabilized finite elements is used to solve the non-linear Stokes problem. The VOF function is computed on a structured grid with a high resolution. The algorithm is stable for Courant numbers larger than unity and conserves mass to a high accuracy. To demonstrate the potential of the algorithm, we apply it to reconstructed Late-glacial states of a small valley glacier, Vadret Muragl, in the Swiss Alps.