Stabilized adaptive finite elements for laminar burners in 3-d

We describe recent developments in the design and implementation of finite element methods for the compressible Navier-Stokes equations modeling chemically reactive flows. The emphasize is on the low-Mach number regime including the limit case of incompressible flow. The most important ingredients are appropriate finite element discretizations, residual driven a posteriori mesh refinement, fully coupled defect-correction iteration for linearization, and optimal multigrid preconditioning. The potential of automatic mesh adaptation together with multilevel techniques is illustrated by 2D and 3D simulations of laminar methane combustion including detailed reaction mechanisms