Discontinuous Galerkin methods with Trefftz approximations
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摘要
We present a novel Discontinuous Galerkin Finite Element Method for wave propagation problems. The method employs space–time Trefftz basis functions that satisfy the underlying partial differential equations and the respective interface boundary conditions exactly in an element-wise fashion. The basis functions can be of arbitrarily high order and we demonstrate spectral convergence in the space–time L2-norm. Therefore high order time integration is an inherent property of the method and clearly sets it apart from methods that employ a high order approximation in space only.
论文关键词:Discontinuous Galerkin method,Finite element method,Trefftz method,Higher order time integration,Electrodynamics,Wave propagation
论文评审过程:Received 15 July 2013, Revised 17 January 2014, Available online 31 January 2014.
论文官网地址:https://doi.org/10.1016/j.cam.2014.01.033