Large Eddy Simulations (LES) of turbulent premixed flames in the flamelet regime are carried out using a new subgrid combustion model. This model explicitly incorporates the effects of large-scale advection through a Lagrangian volume transport scheme and the effects of small-scale turbulent stirring and flame propagation (sub.-rid effects) using a one-dimensional linear eddy model. Three-dimensional turbulent stagnation point premixed flames are simulated with the new model and a conventional flame speed model. It is seen that the conventional model implemented using a finite difference discretization of the scalar equations on a typical three-dimensional LES grid is unable to capture the flamelet nature of the stagnation premixed flames. On the other hand, the subgrid model in the new formulation provides enough fine-scale resolution to accurately capture the flamelet nature of undisturbed laminar flame propagation and small scale wrinkling of the flame surface. As a result, the intermittency associated with flame turbulence interactions (i.e. flame generated turbulence) is better predicted by the new approach. Transition from wrinkled flamelet to corrugated flamelet combustion is also well captured by the new approach. Though the new approach is implemented here using a single evolution equation for the self-propagating flame surface, it can also be extended to deal with diffusive scalar fields. The results shown here also illustrate the need for multi-level discretization that can simultaneously capture flames that have thicknesses much smaller than the typical LES grid spacing, the small subgrid scale wrinkling and large scale advection.