In order to reduce the error within the numerical evaluation of the chemical source term, spatial interpolation based on the discrete cell centered scalar quantities is applied. By that, their subgrid evolution is approximated which serves for a more accurate evaluation of the source terms dependency on transported scalars whose non-linearity is the major cause of errors. A detailed analysis is performed to assess this approach within the context of premixed combustion simulations. Besides an a priori analysis, simulations of one-dimensional flame propagation as well as two-dimensional flame-vortex-interactions are used to quantify the gain with respect to the computed flame speed and the corresponding accuracy of the predicted flame dynamics. For the application within realistic applications it is demonstrated how the method can be combined with the artificially thickened flame model for large eddy simulations. This includes the theoretical derivation, simple testcases for a detailed verification and assessment, and finally the simulations of a turbulent swirl burner, where also the computational efficiency is addressed. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.