局部隐式有限元法

Locally Implicit Finite Element Method

局部隐式有限元法是在一般有限元法的基础上，兼容了ＴＶＤ差分格式和有限体积法的某些特点，形成的一种新型算法。本文针对Ｂｕｒｇｅｒｓ方程推导出了局部隐式有限元法并进行了稳定性分析。认为局部隐式有限元法是一种绝对稳定的方法，且具有快速收敛的性质，是求解非线性偏微分方程的一种有效的数值算法。

A new algorithm, locally twitch finite element method is developed on the base of the general finite element method, mixed with total-variation-diminishing(TVD) scheme and the finite volume method. This paper gives the locally implicit finite element method and the locally stability analysis for the non-linear model equation, Burgers' equation. Locally implicit finite element method is a satisfactory numerical method to solve non-linear partial differential equations for its unconditional stability and its high rate of convergence.