{"product_id":"high-order-discontinuous-galerkin-methods-for-the-maxwell-equations-9786131500206","title":"High-order discontinuous galerkin methods for the maxwell equations","description":"\u003cp\u003e • Author(s): Fahs-H\u003cbr\u003e • Publisher: Univ Europeenne\u003cbr\u003e • Publisher Imprint: Univ Europeenne\u003cbr\u003e • BISAC: General\u003c\/p\u003e\u003cp\u003eThis work is concerned with the development of a high-order discontinuous Galerkin time-domain (DGTD) method for solving Maxwell's equations on non-conforming simplicial meshes. First, we present a DGTD method based on high-order nodal basis functions for the approximation of the electromagnetic field within a simplex, a centered scheme for the calculation of the numerical flux at an interface between neighbouring elements, and a second-order leap-frog time integration scheme. Next, to reduce the computational costs of the method, we propose a hp-like DGTD method which combines local h-refinement and p-enrichment. Then, we report on a detailed numerical evaluation of the DGTD methods using several propagation problems. Finally, in order to improve the accuracy and rate of convergence of the DGTD methods previously studied, we study a family of high-order explicit leap-frog time schemes. These time schemes ensure the stability under some CFL-like condition. We also establish rigorously the convergence of the semi-discrete approximation to Maxwell's equations and we provide bounds on the global divergence error.\u003c\/p\u003e","brand":"Atlantic Books","offers":[{"title":"Paperback","offer_id":46472991178903,"sku":"9786131500206","price":7242.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9786131500206.jpg?v=1766257970","url":"https:\/\/atlanticbooks.com\/products\/high-order-discontinuous-galerkin-methods-for-the-maxwell-equations-9786131500206","provider":"Atlantic Books","version":"1.0","type":"link"}