Abstract: A hybrid monotonous finite element algorithm is developed in the present paper,based on a second-order-accurate finite elment scheme and a first-order-accuratemonotonous one derived from the former by a unilateral lumping procedure in onedimensional case. The switch functions for the two dimensional Euler equation systemare constructed locally, based on the gradient of the flow field, with specialconsideration on the information from neighboring elements.Examples show that the ew scheme can eliminate oscillations near strong shocks obviously.

Key words: finite element, hybrid scheme, shocks