Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 1 March 2021Accepted: 27 August 2021Published online: 10 February 2022Keywordsspectral element method, Gauss--Lobatto quadrature, superconvergence, wave equation, parabolic equations, linear Schrödinger equationAMS Subject Headings65M60, 65M15, 65M06Publication DataISSN (...

Abstract. The purpose of this paper is twofold: to give a brief yet comprehensive description of the spectral element and semi-Lagrangian methods, and to introduce a new method arrived at by fusing both of these impressive methods. The practical aspects of both methods are described in detail by their implementation on the 2D shallow water equations. These equations have been used customarily t...