求解双曲守恒律方程的高次有限元方法

FINITE ELEMENT METHODS WITH A HIGH ORDER FOR SOLVING CONSERVATION LAWS

将Galerkin高次有限元应用于双曲守恒律的Hamilton Jacobi方程 ,得到了求解双曲守恒律的一类数值格式。这类格式在CFL条件下具有TVD性质 ,在更强的条件下 ,其半离散格式的数值解收敛于守恒律方程的熵解。数值结果表明 ,这类格式具有较高的分辨激波的能力。

A class of numerical schemes are presented for solving conservation laws which are obtained by applying Galerkin finite element with a high order to Hamilton Jacobi equations. These schemes satisfy TVD properties under CFL condition. If these schemes are required more limitations, semi discrete schemes among them are entropy schemes. Numerical tests are given, which illustrates these schemes with a high resolution for shock waves.