Nodal high-order methods on unstructured grids

By Jan S. Hesthaven, Tim Warburton. 2002

793 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mechanics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/f37a29256a986c7dbc024cfb9fca0e1715d9b9cd

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In Atomic and Molecular Physics, and Optics

In Computational Mechanics

In Electrical and Electronic Engineering

Citations in the corpus

Convergence and stability of a discontinuous galerkin time-domain method for the 3D heterogeneous maxwell equations on unstructured meshes (2005, methodology): “The convergence result is slightly weaker than available results for general triangulations and upwind (or monotone) fluxes [5, 9] and the same as one given recently [11] (this is also the case for the error bound on the divergence of the fields).”
The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems (2007, positive): “We assume throughout that nodal bases [13] are used to span the approximating and weighting Galerkin spaces.”
Discontinuous Galerkin Finite Element Method for the Wave Equation (2006, methodology): “Hesthaven and Warburton [13] used the same approach to implement high-order methods for Maxwell’s equations in first-order hyperbolic form.”
Locally divergence-free discontinuous Galerkin methods for the Maxwell equations (2004, methodology): “In [15], the discontinuous Galerkin method with the standard piecewise polynomial spaces is used to solve Maxwell equations on unstructured meshes.”
A New Class of High-Order Energy Stable Flux Reconstruction Schemes (2011, background): “Such schemes have become known as nodal DG methods, an exposition of which can be found in the recent textbook by Hesthaven and Warburton [4], as well as in various articles by the same authors [5, 6].”
Higher Order Time Stepping for Second Order Hyperbolic Problems and Optimal CFL Conditions (2008, background): “Several approaches lead naturally to problems of the form (2), among which • variational finite differences [10, 12, 1], • finite element methods [8, 7], • mixed finite element methods [9, 21], • conservative discontinuous Galerkin methods [17, 15].”
Nodal discontinuous Galerkin methods on graphics processors (2009, positive): “Remarkably, the same is also true of the DG discretization of the operator [10].”
High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces (2004, methodology): “Recently, a promising high-order nodal method on fully unstructured grids has been developed by means of a discontinuous Galerkin formulation and a penalty method for boundary conditions [38].”
PyCUDA and PyOpenCL: A scripting-based approach to GPU run-time code generation (2009, methodology): “The computation was performed at fourth order on a mesh of 78745 elements using an incident-ﬁeld formulation [17] and characteristic absorbing boundary conditions.”
Energy conserving local discontinuous Galerkin methods for wave propagation problems (2013, positive): “They were originally devised to solve hyperbolic conservation laws with only first order spatial derivatives, e.g. [8, 9, 10, 12, 13].”