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**Space–time SUPG formulation of the shallow-water equations.**
*(English)*
Zbl 1427.35212

Summary: We present a new space–time SUPG formulation of the shallow-water equations. In this formulation, we use a stabilization parameter that was introduced for compressible flows and a new shock-capturing parameter. In the context of two test problems, we evaluate the performance of the new shock-capturing parameter. We also evaluate the performance of the space–time SUPG formulation compared to the semi-discrete SUPG formulation, where the system of semi-discrete equations is solved with the central-difference (Crank–Nicolson) time-integration algorithm.

### MSC:

35Q35 | PDEs in connection with fluid mechanics |

76M10 | Finite element methods applied to problems in fluid mechanics |

### Keywords:

shallow-water equations; finite element method; space; time method; SUPG formulation; shock-capturing parameter
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\textit{S. Takase} et al., Int. J. Numer. Methods Fluids 64, No. 10--12, 1379--1394 (2010; Zbl 1427.35212)

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### References:

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