A numerical method to simulate premixed combustion is analyzed. It consists of a Cartesian cut-cell flow solver for compressible viscous flows coupled with a level-set method which solves the G-equation to describe the kinematics of the premixed flame. The coupling of the two solvers is achieved via a dual hierarchical dynamic adaptive-mesh framework. Both solvers operate on different Cartesian hierarchical meshes sharing a common background grid level through which they are connected. For the flow solver, feature- and G-based adaptive mesh refinement is taken advantage of, while a uniform high-resolution grid is used for the level-set solver. The heat release due to combustion is described by a source-term formulation by which the reaction rate profile of the premixed flame can be attached to the flame front, the motion of which is governed by the G-equation. A flame-vortex interaction problem is discussed in detail to validate the proposed methodology and to demonstrate the benefits of solution-adaptive mesh refinement in the context of the level-set approach for premixed combustion. After a forced laminar Bunsen flame is considered as an example for attached flames, the coalescence of two spherical flame kernels is simulated to assess the performance of the method and the potential savings in terms of computational costs for three-dimensional problems. The results of the test problems show the artificial thickening of the flame and numerical errors in the level-set solution on coarser grids to possess a comparatively small impact on the overall accuracy. The best findings in the sense of efficiency and physical quality are achieved by the combined feature-/G-based adaptation method. (C) 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved.