Finite‐amplitude solutions to subcritical, time‐dependent, double‐diffusive convection (D.D.C.) applicable for magma chambers are obtained by a two‐dimensional, finite‐element method based on stream‐function, temperature and compositional fields. Grid‐refinement is used for resolving the disparately‐scaled thermal and chemical boundary layers present for large ratios of the thermal to chemical diffusivity (Lewis number) characteristic of magmas. The occurrence of layered convection depends strongly on the initial conditions of the temperature and composition. It is shown that in the infinite Prandtl number limit a local transition from a diffusive to a finger‐like regime can take place for large enough Lewis numbers. This time‐dependent finding suggests that a strict categorization of D.D.C. into the finger and diffusive regimes requires modification in geological applications.