Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids

By Bernardo Cockburn, Guido Kanschat, Ilaria Perugia, Dominik Schötzau. SIAM Journal on Numerical Analysis, 2001

362 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dfc9e0684140a5cd5a8b7c8d116495d849a6b63e

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In Computational Mechanics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

On 2D elliptic discontinuous Galerkin methods (2006, background): “This observation appears to be consistent with observations made in [13, 14] where stabilisation is required in the weak enforcement of boundary conditions.”
The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems (2007, neutral): “Clearly, there is plenty of flexibility in choosing appropriate values for switches which satisfy the rule (4.1); see [ 9 ], for instance.”
A NUMERICAL STUDY OF UNIFORM SUPERCONVERGENCE OF LDG METHOD FOR SOLVING SINGULARLY PERTURBED PROBLEMS (2009, methodology): “Key words: Singularly perturbed problems, Local discontinuous Galerkin method, Numerical fluxes, Uniform superconvergence.”
Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems (2001, background): “In recent years there has been renewed interest in this class of techniques, stimulated by the computational convenience of DGFEMs due to a high degree of locality, the need to approximate advectiondominated diffusion problems without excessive numerical stabilization, the necessity to accommodate h”
A projection-based error analysis of HDG methods (2010, methodology): “…ﬂuxes by satisfying This should be compared with the deﬁnition of their numerical trace [11] Besides the projections used to carry out the analysis of the DG methods in [8], [6] and [13], we have the projections used in [9] to analyze an HDG type method called single-face hybridizable (SFH) method.”
Local Discontinuous Galerkin Methods for the Stokes System (2002, methodology): “We pick a direct extension of the choice of numerical fluxes for the Laplace operator considered in [8] and [13].”
High‐order continuous and discontinuous Galerkin methods for wave problems (2013, background): “There are several possible choices of the switches, always satisfying Sij + Sji = 1, see [34, 56] for details.”
Approximation of the Velocity by Coupling Discontinuous Galerkin and Mixed Finite Element Methods for Flow Problems (2002, methodology): “Unlike the approach used in [7], we do not eliminate the variable that approximates u and rewrite the method in its “primal form”; instead, we use a classical mixed setting and obtain estimates for both the approximations of u and p. Such an approach has already been used in [16] and [ 22 ], where i”
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems (2001, methodology): “Thus, Section 2 is mainly related to the papers [49] and [48]; Section 3 to the papers [46], [41] and [51]; Section 4 to the papers [32], [42], and [43]; Section 5 to [107], [50], [33], and [88]; Section 6 to [72], [82] and [71]; finally, Section 7 to [47].”