We consider the Korteweg–de Vries equation posed on a spatial interval whose endpoints evolve in time. The spatial discretization is carried out by a Galerkin finite-element formulation based on B-spline basis functions, whereas temporal integration uses the Crank–Nicolson scheme. Benchmark tests confirm that the proposed algorithm attains high accuracy while remaining computationally efficient. The results illustrate that the method robustly captures wave propagation in domains with moving boundaries.