RESEARCH ON NON OSCILLATION, PARAMETER FREE FINITE ELEMENT SCHEME 1)
关于无振荡、无自由参数有限元格式的研究

A finite element modified equation is estabished by using the finite element Taylor weak statement for hyperbolic conservation laws and various finite element numerical schemes are obtained by means of reasonably choosing the coefficient of the expansional expression. The relations between the coefficients of the differential terms of the finite element modified equation and stability, dissipation error and dispersion error of finite element schemes are investigated by means of stability analysis. These relations are in conformity with NND schemes developed by reference for finite difference method. For a selected finite element scheme, the spurious oscillation of solution may be controlled by regulating the CFL number and make schemes free of parameter. Finally, linear and nonlinear numerical examples are carried out for verifications and the conclusion is applied to the solution of two and three dimensional Euler equations.