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

Rémi Abgrall

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.

  • Keywords

Discontinuous finite element methods, residual distribution schemes, hyperbolic problems, nonlinear stabilisation.

  • AMS Subject Headings

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

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-2-32, author = {}, 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 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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