A Residual Distribution Method Using Discontinuous Elements for the Computation of Possibly Non Smooth Flows
Year: 2010
Author: Rémi Abgrall
Advances in Applied Mathematics and Mechanics, Vol. 2 (2010), Iss. 1 : pp. 32–44
Abstract
In this paper, we describe a residual distribution (RD) method where, contrarily to "standard" this type schemes, the mesh is not necessarily conformal. It also allows using discontinuous elements, contrary to the "standard" case where continuous elements are requested. Moreover, if continuity is forced, the scheme is similar to the standard RD case. Hence, the situation becomes comparable with the Discontinuous Galerkin (DG) method, but it is simpler to implement than DG and has guaranteed $L^∞$ bounds. We focus on the second-order case, but the method can be easily generalized to higher degree polynomials.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.09-m0934
Advances in Applied Mathematics and Mechanics, Vol. 2 (2010), Iss. 1 : pp. 32–44
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Discontinuous finite element methods residual distribution schemes hyperbolic problems nonlinear stabilisation.