A hybrid finite element scheme for inviscid supersonic flows

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