Discontinuous hp-finite element methods for advection-diffusion problems

By Paul Houston, Christoph Schwab, Endre Süli. 2000

97 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a12b1a8feadb67591e4121b0989883b9274a42f1

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In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems (2001, methodology): “[22], [23] studied several variations of the original method of Bassi and Rebay; Oden, Babuika, and Baumann [59] studied the DG method of Baumann and Oden; Riviere and Wheeler [63] and Riviere, Wheeler, and Girault [64] analyzed several variations of the DG method of Baumann and Oden; Becker and Han”
A numerical PDE approach for pricing callable bonds (2001, background): “Note that these conditions have been generalized in Houston et al. (2000). For the CIR model this is just our condition that 2κθ/σ2 ≥ 1.”
Discontinuous Galerkin methods (2003, methodology): “Let us end this paper by pointing out that a very important issue that has not been touched in this paper is the ease with which these methods can handle hp-adaptive strategies [16–18, 43, 44, 47–50, 55–58, 74, 75] and can be coupled with already existing methods [2, 29, 69].”
A finite volume discontinuous Galerkin scheme¶for nonlinear convection–diffusion problems (2002, methodology): “We estimate the individual terms in (4.15) in a similar way to that in [ 24 ].”
Analysis of semi-implicit DGFEM for nonlinear convection–diffusion problems on nonconforming meshes ☆ (2007, result): “, [1], [3], [5], [4], [7], [14], [15], [16], [19], [23], [24], [25], [27], [29], [31].”
Error Estimates of the Discontinuous Galerkin Method for Nonlinear Nonstationary Convection-Diffusion Problems (2005, background): “Some aspects of the DGFEM are investigated, for example, in [1, 5, 6, 12, 14, 16, 19, 26, 28, 31, 33].”
A Priori Error Analysis for the hp-Version of the Discontinuous Galerkin Finite Element Method for the Biharmonic Equation (2003, background): “As in [11], we shall assume that there exists a constant ρ > 0 such that for any pair of elements K and K ′ which share some face e ∈ E one has ρ−1pK′ 6 pK 6 ρpK′ .”
Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems (2001, background): “5), in the case of homogeneous boundary conditions, is shown in [17] (see also [18]).”
HP DISCONTINUOUS GALERKIN APPROXIMATIONS FOR THE STOKES PROBLEM (2002, background): “, [19].”
Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality (2002, unknown): “We shall now illustrate these points through a simple numerical example using the streamline diffusion finite element method (SDFEM) with continuous piecewise polynomials of degree k = 1 (see Houston et al. (2000a) for details).”