Titlebook: Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equati; 2012 John H Barrett Xiaobing Feng,Oh

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,A Local Timestepping Runge–Kutta Discontinuous Galerkin Method for Hurricane Storm Surge Modeling, an RKDG shallow water simulator, developed by the author and collaborators over a period of several years. We demonstrate that, for a specific hurricane, namely Hurricane Ike, the LTS method can reduce parallel run-times by nearly a factor of two with no degradation in accuracy.

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Error Control for Discontinuous Galerkin Methods for First Order Hyperbolic Problems,cial case of the mesh having one characteristic face per element is the focus of discussion, although some comments on possible extensions to general meshes are given. Numerical experiments verify the reliability and the efficiency of the estimator.

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Adaptivity and Error Estimation for Discontinuous Galerkin Methods,7; Adjerid and Baccouch, J. Sci. Comput. 38(1):15–49, 2008; Adjerid and Baccouch Comput. Methods Appl. Mech. Eng. 200:162–177, 2011) for hyperbolic problems on adaptively refined unstructured triangular meshes. A local error analysis allows us to construct asymptotically correct a posteriori error e

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,A Local Timestepping Runge–Kutta Discontinuous Galerkin Method for Hurricane Storm Surge Modeling,s method to the modeling of hurricane storm surge. Modeling storm surge requires the numerical solution of the shallow water equations with wind and atmospheric pressure forcing, over complex domains which include wet and dry regions. The RKDG method is well suited for these applications; however, w

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Virtual Element and Discontinuous Galerkin Methods,ement approach. They combine the ductility of mimetic finite differences for dealing with rather weird element geometries with the simplicity of implementation of Finite Elements. Moreover, they make it possible to construct quite easily high-order and high-regularity approximations (and in this res