TVD Finite Element Scheme for Hyperbolic Systems of Conservation Laws
K. Kakuda;  A. Seki;  Y. Yamauchi

doi:10.3970/cmes.2010.069.281
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 69, No. 3, pp. 281-306, 2010
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Keywords Finite element, Petrov-Galerkin method, exponential weighting functions, flux-limiter, TVD.
Abstract A finite element scheme based on the concept of TVD (total variation diminishing) with a flux-limiter for the hyperbolic systems of conservation laws is presented. The numerical flux is formulated effectively by the weighted integral form using exponential weighting functions. The TVD finite element scheme is applied to a Riemann problem, namely the shock-tube problem, for the Euler system of equations. Numerical results demonstrate the workability and the validity of the present approach through comparison with the exact solutions.
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