Volume 2, Issue 1
A Residual Distribution Method Using Discontinuous Elements for the Computation of Possibly Non Smooth Flows

Adv. Appl. Math. Mech., 2 (2010), pp. 32-44.

Published online: 2010-02

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• 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.

65N12, 65N08, 65N30, 76-04

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@Article{AAMM-2-32, author = {Abgrall , Rémi}, title = {A Residual Distribution Method Using Discontinuous Elements for the Computation of Possibly Non Smooth Flows}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2010}, volume = {2}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m0934}, url = {http://global-sci.org/intro/article_detail/aamm/199.html} }
TY - JOUR T1 - A Residual Distribution Method Using Discontinuous Elements for the Computation of Possibly Non Smooth Flows AU - Abgrall , Rémi JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 32 EP - 44 PY - 2010 DA - 2010/02 SN - 2 DO - http://doi.org/10.4208/aamm.09-m0934 UR - https://global-sci.org/intro/article_detail/aamm/199.html KW - Discontinuous finite element methods, residual distribution schemes, hyperbolic problems, nonlinear stabilisation. AB -

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.

Rémi Abgrall. (1970). A Residual Distribution Method Using Discontinuous Elements for the Computation of Possibly Non Smooth Flows. Advances in Applied Mathematics and Mechanics. 2 (1). 32-44. doi:10.4208/aamm.09-m0934
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