A local refinement method is used to numerically predict the propagation and extinction conditions of a premixed flame in a channel considering a thermodiffusive model. A local refinement method is employed because of the numerous length scales that characterize this phenomenon. The time integration is self adaptive and the solution is based on a multigrid method using a zonal mesh refinement in the flame reaction zone. The objective is to determine the conditions of extinction which are characterized by the flame structure and its properties. We are interested in the following properties: the curvature of the flame, its maximum temperature, its speed of propagation and the distance separating the flame from the wall. We analyze the influence of heat losses at the wall through the thermal conductivity of the wall and the nature of the fuel characterized by the Lewis number of the mixture. This investigation allows us to identify three propagation regimes according to heat losses at the wall and to the channel radius. The results show that there is an intermediate value of the radius for which the flame can bend and propagate provided that its curvature does not exceed a certain limit value. Indeed, small values of the radius will choke the flame and extinguish it. The extinction occurs if the flame curvature becomes too small. Furthermore, this study allows us to predict the limiting values of the heat loss coefficient at extinction as well as the critical value of the channel radius above which the premixed flame may propagate without extinction. A dead zone of length 2-4 times the flame thickness appears between the flame and the wall for a Lewis number (Le) between 0.8 and 2. For small values of Le, local extinctions are observed.