Trigonometric WENO Schemes for Hyperbolic Conservation Laws and Highly Oscillatory Problems (Communications in Computational Physics, 2010)
In this paper, we use trigonometric polynomial reconstruction, instead ofalgebraic polynomial reconstruction, as building blocks for the weighted essentiallynon-oscillatory (WENO) finite difference schemes to solve hyperbolic conservationlaws and highly oscillatory problems. The goal is to obtain robust and high orderaccurate solutions in smooth regions, and sharp and non-oscillatory shock transitions.Numerical results are provided to illustrate the behavior of the proposed schemes.