A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems

By Slimane Adjerid, Karen D. Devine, Joseph E. Flaherty, Lilia Krivodonova. 2002

240 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/25bdc142022bd613f6d4e523c982cb48ad579923

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In Computational Mechanics

In Numerical Analysis

Citations in the corpus

Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws (2004, methodology): “As noted, smooth DGM solutions of (4) exhibit a strong superconvergence phenomena at outflow boundaries [1, 26] such that”
Numerical resolution of discontinuous Galerkin methods for time dependent wave equations (2011, background): “[2] proved that the DG solution of the ordinary differential equation (ODE) u0 f(u) = 0 is superconvergent of order 2k + 1 at the downwind end of each element while maintaining an order of k + 2 at the remaining Radau points.”
A posteriori error estimation and dynamic adaptivity for symmetric discontinuous Galerkin approximations of reactive transport problems (2006, unknown): “A posteriori error estimators can be used to signify where modifications in discretization parameters need to be made, thus achieving adaptivity, in particular, goal-oriented hp-adaptivity [31,39,20,8,5–7,19,21–23,26,32,35,38,40,44,27,18,4,2,3], see also [57,9,13] and references therein.”
A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems (2002, methodology): “[1] to multidimensional hyperbolic problems on rectangular meshes.”
Adaptive mesh generation for curved domains (2005, methodology): “The procedure takes advantage of the superconvergence properties of the DG method [1] and monitors estimates of the convergence rate over the domain.”
An adaptive discretization of shallow‐water equations based on discontinuous Galerkin methods (2006, background): “A complete description of the test case and of the available experimental data can be found in Reference [25].”
High-order h-adaptive discontinuous Galerkin methods for ocean modelling (2007, methodology): “The discontinuous Galerkin (DG) method has become a very attractive method especially for advection-dominated problems (e.g. Cockburn et al. 2000; Adjerid et al. 2002; Bassi and Rebay 1997).”
Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent Developments (2014, unknown): “In [2, 3], Adjerid et al.”
Superconvergence of discontinuous Galerkin solutions for a nonlinear scalar hyperbolic problem (2006, methodology): “[1] used the limiting technique of Biswas et al.”