A finite element semi-Lagrangian method with L interpolation
نویسندگان
چکیده
High-order accurate methods for convection-dominated problems have the potential to reduce the computational effort required for a given order of solution accuracy. The state of the art in this field is more advanced for Eulerian methods than for semi-Lagrangian (SLAG) methods. In this paper, we introduce a new SLAG method that is based on combining the modified method of characteristics with a high-order interpolating procedure. The method employs the finite element method on triangular meshes for the spatial discretization. An L interpolation procedure is developed by tracking the feet of the characteristic lines from the integration nodes. Numerical results are illustrated for a linear advection–diffusion equation with known analytical solution and for the viscous Burgers’ equation. The computed results support our expectations for a robust and highly accurate finite element SLAG method. Copyright © 2012 John Wiley & Sons, Ltd.
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