Local Discontinuous Galerkin Methods for the Stokes System

By Bernardo Cockburn, Guido Kanschat, Dominik Schötzau, Christoph Schwab. SIAM Journal on Numerical Analysis, 2002

297 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/1ab5313132a1e0e4a11c170e794ed0b841970339

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In Computational Mechanics

In Numerical Analysis

Citations in the corpus

Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations (2009, methodology): “LDG methods for the Stokes system were introduced in [33].”
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems (2001, background): “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].”
Divergence free Virtual Elements for the Stokes problem on polygonal meshes (2015, background): “For such a problem, a few other numerical schemes using polytope meshes have been proposed, see for example [5,27,38,52].”
A Note on Discontinuous Galerkin Divergence-free Solutions of the Navier–Stokes Equations (2007, methodology): “In [16], DG methods for the Stokes equations were considered.”
IsoGeometric Analysis: Stable elements for the 2D Stokes equation (2011, background): “For that reason classical (discontinuous) Raviart–Thomas and Nédélec elements are not popular in the finite element approximations of the Stokes problem, since they lead to non-conforming schemes, though interesting results are proposed in [9, 15, 16].”
On 2D elliptic discontinuous Galerkin methods (2006, methodology): “We also note that the LDG has been successfully applied in the solution of non-trivial elliptic problems such as the Stokes system [15] and the Oseen equations [16].”
Discontinuous Galerkin methods for incompressible elastic materials (2006, methodology): “In contrast, the approaches used, for example, in [2] and [13] (for second order equations), in [9] (for the Stokes system), and more recently in [8] (for the Navier-Stokes equations) all rely on the elimination of one of the variables and cannot easily obtain error estimates in negative-order norms”
A locally conservative LDG method for the incompressible Navier-Stokes equations (2004, methodology): “A similar coercivity result involving also the discrete velocity gradient was used in [9] and [8].”
hp analysis of a hybrid DG method for Stokes flow (2013, unknown): “The sharp estimate for the inf-sup constants in turn allows to derive a-priori estimates, which are optimal with respect to the meshsize and only slightly sub-optimal with respect to the polynomial degree.”