To control and reduce emissions for combustion devices, numerical simulations are becoming increasingly important. In this study, numerical simulations of a domestic methane burner are performed to predict the temperature profile and the formation of carbon monoxide and nitric oxide. A detailed reaction scheme, as well as a detailed transport model was used in this two-dimensional study. We consider premixed laminar flames at low flow speed. The numerical simulations are performed with the object-oriented C++ code Gascoigne (Becker and Braack, 2001), which was developed recently and has the adaptive-gridding capability allowing minimization of the error in the numerical simulation with respect to certain functionals, for example, local values of species mass fraction and mean value of temperature or heat release. A comparison with experiments as well as a parametric study aimed at the minimization of pollutants were carried out. The optimal parameters to guarantee a good compromise between flame stability and toxic emissions are presented.