The finite element method for hyperbolic conservation laws

CHINESE JOURNAL OF COMPUTATIONAL PHYSICS ›› 1999, Vol. 16 ›› Issue (5): 457-466.

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The finite element method for hyperbolic conservation laws

Yu Xijun¹, Fu Hongyuan¹, Chang Qianshun²

1. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088;
2. Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080

Received:1998-04-27 Revised:1999-02-10 Online:1999-09-25 Published:1999-09-25

Abstract

Abstract: A scheme is outlined for solving hyperbolic conservation laws by finite element method of piecewise linear interpolations. It is different from the discontinuous finite element on the boundaries of neighboring cells to solve Riemann problems that the scheme is designed to solve hyperbolic conservation laws based on the Hamilton Jacobi equations. Under the CFL condition, the scheme is proved that it satisfies the maximal principle and is a TVD scheme. Numerical examples are given and discussed.

Key words: Finite element method, Hyperbolic conservation laws, Hamilton Jacobi equations

CLC Number:

O351.3

Yu Xijun, Fu Hongyuan, Chang Qianshun. The finite element method for hyperbolic conservation laws[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1999, 16(5): 457-466.

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The finite element method for hyperbolic conservation laws

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