Characteristic-Galerkin and Galerkin/least-squares space-time formulations for the advection-diffusion equation with time-dependent domains

O. Pironneau; J. Liou; T. Tezduyar

doi:10.1016/0045-7825(92)90116-2

Characteristic-Galerkin and Galerkin/least-squares space-time formulations for the advection-diffusion equation with time-dependent domains

O. Pironneau^*, J. Liou, T. Tezduyar

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

70 Citations (Scopus)

Abstract

For the advection-diffusion equation, the characteristic-Galerkin formulations are obtained by temporal discretization of the total derivative. These formulations, by construction, are Eulerian-Lagrangian, and therefore can handle time-dependent domains without difficulty. The Galerkin/least-squares space-time formulation, on the other hand, is written over the space-time domain of a problem, and therefore can handle time-dependent domains with no implementational difficulty. The purpose of this paper is to compare these two formulations based on error estimates and numerical performance, in the context of the advection-diffusion equation.

Original language	English
Pages (from-to)	117-141
Number of pages	25
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	100
Issue number	1
DOIs	https://doi.org/10.1016/0045-7825(92)90116-2
Publication status	Published - 1992 Oct
Externally published	Yes

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
Physics and Astronomy(all)
Computer Science Applications

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10.1016/0045-7825(92)90116-2

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title = "Characteristic-Galerkin and Galerkin/least-squares space-time formulations for the advection-diffusion equation with time-dependent domains",

abstract = "For the advection-diffusion equation, the characteristic-Galerkin formulations are obtained by temporal discretization of the total derivative. These formulations, by construction, are Eulerian-Lagrangian, and therefore can handle time-dependent domains without difficulty. The Galerkin/least-squares space-time formulation, on the other hand, is written over the space-time domain of a problem, and therefore can handle time-dependent domains with no implementational difficulty. The purpose of this paper is to compare these two formulations based on error estimates and numerical performance, in the context of the advection-diffusion equation.",

author = "O. Pironneau and J. Liou and T. Tezduyar",

note = "Funding Information: This research was sponsored by the US Army (under contract DAAL03-89-C-0038), NSF (under grant MSM-8796352), and INRIA, France. We thank Marek Behr for generating the mesh used.",

year = "1992",

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doi = "10.1016/0045-7825(92)90116-2",

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AU - Pironneau, O.

AU - Liou, J.

AU - Tezduyar, T.

N1 - Funding Information: This research was sponsored by the US Army (under contract DAAL03-89-C-0038), NSF (under grant MSM-8796352), and INRIA, France. We thank Marek Behr for generating the mesh used.

PY - 1992/10

Y1 - 1992/10

N2 - For the advection-diffusion equation, the characteristic-Galerkin formulations are obtained by temporal discretization of the total derivative. These formulations, by construction, are Eulerian-Lagrangian, and therefore can handle time-dependent domains without difficulty. The Galerkin/least-squares space-time formulation, on the other hand, is written over the space-time domain of a problem, and therefore can handle time-dependent domains with no implementational difficulty. The purpose of this paper is to compare these two formulations based on error estimates and numerical performance, in the context of the advection-diffusion equation.

AB - For the advection-diffusion equation, the characteristic-Galerkin formulations are obtained by temporal discretization of the total derivative. These formulations, by construction, are Eulerian-Lagrangian, and therefore can handle time-dependent domains without difficulty. The Galerkin/least-squares space-time formulation, on the other hand, is written over the space-time domain of a problem, and therefore can handle time-dependent domains with no implementational difficulty. The purpose of this paper is to compare these two formulations based on error estimates and numerical performance, in the context of the advection-diffusion equation.

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Characteristic-Galerkin and Galerkin/least-squares space-time formulations for the advection-diffusion equation with time-dependent domains

Abstract

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