Develop and evaluate a residual-based a posteriori error estimator for parabolic partial differential equations formulated on closed, stationary surfaces.
Discretized space using the surface finite element method on closed stationary surfaces.
Discretized time using the implicit backward Euler method.
Constructed a space-time adaptive refinement algorithm driven by the derived error indicator.
Demonstrated that the error indicator reliably bounds error quantities globally from above and below in space.
Established that the indicator bounds errors globally from above and locally from below in time.
Confirmed the theoretical error bounds and adaptive efficiency through numerical experiments.