In order to investigate the influences of the finite element method（FEM）

finite volume method（FVM）

and the grid structures on the simulation of dielectric barrier columnar discharges in atmospheric helium

we established a twodimensional（2D） fluid model. Firstly

we calculated the current waveforms and 2D electron density distributions of the discharge; secondly

we comparatively studied the performances of the FEM and the FVM based on convergence plots

number of iterations

and computation time; finally

we comparatively studied discharge morphology and sequence obtained by the two algorithms based on the 2D electron density distributions and the experimental results. The results show that the discharge evolves from a uniform pattern into a columnar one in the unstable initial stage

and it reaches a steady columnar discharge at last. The FVM is more stable and less time consuming than the FEM. And the variation of grid structure affects the discharge morphology obtained by the FVM. Under the square grid structure

the columnar discharge obtained by the FVM coincides with the experimental results.