Using Arbitrary Lagrangian-Eulerian method on an adaptive moving unstructured mesh, we carry out nu- merical simulations for a rising bubble interacting with a solid wall. Driven by the buoyancy force, the axisymmetric bubble rises in a viscous liquid toward a horizontal wall, with impact on and possible bounce from the wall. First, our simulation is quantitatively validated through a detailed comparison between nu- merical results and experimental data. We then investigate the bubble dynamics which exhibits four different behaviors depending on the competition among the inertial, viscous, gravitational, and capillary forces. A phase diagram for bubble dynamics has been produced using the Ohnesorge number and Bond number as the two dimensionless control parameters. Finally, we turn to the late stage of the bubble rise characterized by a small flux of liquid escaping from the thin film between the wall and bubble. Since the thin film dynamics can be accurately described by the lubrication approximation, we carry out numerical simulations to compare the simulation results with the predictions of the lubrication approximation. Remarkable agreement is obtained to further demonstrate the accuracy of the simulations.