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Homological linear quotients and edge ideal of graphs
No full texthttp://dx.doi.org/10.1017/S0004972712000330
Diophantine transference principle over function fields
No full texthttp://dx.doi.org/10.1017/S000497271200033
A conjecture of Merca on congruences modulo powers of for partitions into distinct parts
No full texthttp://dx.doi.org/10.1017/S000497271200033
Computing points on bielliptic modular curves over fixed quadratic fields
No full texthttp://dx.doi.org/10.1017/S000497271200033
Eventual positivity and asymptotic behaviour for higher-order evolution equations
No full texthttp://dx.doi.org/10.1017/S000497271200033
Weierstrass zeta functions and -adic linear relations
No full texthttp://dx.doi.org/10.1017/S000497271200033
On the Ramsey numbers of tree graphs versus certain generalised wheel graphs
No full texthttp://dx.doi.org/10.1017/S000497271200033
Typhoons and Tigers—flood risk in the Sundarbans
Get PDFThe many small inhabited islands of the Sundabarn region in north east India and Bangladesh, are subject to sea water flooding during cyclones. The objective is to predict flood risk so that improvements to flood defences can be prioritised. There are a few records of flood heights at a very limited set of locations, but there are long term data on cyclones that can be used to drive a simulation model to estimate flood risk at any points in the Sundarbans. The cyclone data is used to fit a stochastic model for cyclones. The cyclone model is combined with a deterministic storm surge model that provides sea level at the boundary of the Sundarbans. A hydraulic routing model, MIKE–21, is then used to predict water levels over a grid of interior points. The combined deterministic surge and routing models are approximated by a regression type model, so the stochastic simulation can quickly generate thousand of years of flood events. Results from a simulation are presented.
References
A. Degenhardt, A. V Metcalfe, and S. Parsons. Combined river and sea flooding. 34th MAFF Conference of River and Coastal Engineers, Keele University, 30 June to 2 July 1999.
S. K. Dube. Prediction of storm surges in the Bay of Bengal. Trop. Cyclone Res. Rev. 1.1 (2012), pp. 67–74. doi: 10.6057/2012TCRR01.08
R. Gayathri, P. K. Bhaskaran, and D. Sen. Numerical study on storm surge and associated coastal inundation for 2009 AILA Cyclone in the head Bay of Bengal. Aquatic Proc. 4 (2015), pp. 404–411. doi: 10.1016/j.aqpro.2015.02.054
A. F. Rahman, D. Dragoni, and B. El-Masri. Response of the Sundarbans coastline to sea level rise and decreased sediment flow: A remote sensing assessment. Remote Sen. Environ. 115.12 (2011), pp. 3121–3128. doi: 10.1016/j.rse.2011.06.019
WCRP Global Sea Level Budget Group. Global sea level budget 1993–present. Earth Sys. Sci. Data 10.3 (2018), pp. 1551–1590. doi: 10.5194/essd-10-1551-201
Optimal Hessian recovery using a biorthogonal system with an application to adaptive refinement
Get PDFWe present a method for recovering the Hessian from a linear finite element approach to achieve a higher rate of convergence. This method uses an -based projection as well as boundary modification to achieve and improve the convergence rate. The projection uses a biorthogonal system to make the computation more numerically efficient. We present numerical examples to illustrate the efficiency and optimality of our approach on different meshes. The performance of our approach on adaptively refined meshes is briefly explored.
References
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R. E. Bank and J. Xu. Asymptotically exact a posteriori error estimators, Part I: Grids with superconvergence. SIAM J. Numer. Anal. 41 (2003), pp. 2294–2312. doi: 10.1137/S003614290139874X
J. H. Bramble and A. H. Schatz. Higher order local accuracy by averaging in the finite element method. Math. Comput. 31.137 (1977), pp. 94–111. doi: 10.2307/2005782.
S. A. Funken and A. Schmidt. Adaptive mesh refinement in 2D—An efficient implementation in Matlab. Comput. Meth. Appl. Math. 20.3 (2020), pp. 459–479. doi: doi:10.1515/cmam-2018-0220.
H. Guo, Z. Zhang, and R. Zhao. Hessian recovery for finite element methods. Math. Comput. 86.306 (2017), pp. 1671–1692. url: https://www.jstor.org/stable/90004689
B.-O. Heimsund, X.-C. Tai, and J. Wang. Superconvergence for the gradient of finite element approximations by L2 projections. SIAM J. Numer. Anal. 40.4 (2002), pp. 1263–1280. doi: 10.1137/S003614290037410X.
Y. Huang and N. Yi. The superconvergent cluster recovery method. J. Sci. Comput. 44 (2010), pp. 301–322. doi: 10.1007/s10915-010-9379-9
M. Ilyas, B. P. Lamichhane, and M. H. Meylan. A gradient recovery method based on an oblique projection and boundary modification. Proceedings of the 18th Biennial Computational Techniques and Applications Conference, CTAC-2016. Ed. by J. Droniou,
M. Page, and S. Clarke. Vol. 58. ANZIAM J. Aug. 2017, pp. C34–C45. doi: 10.21914/anziamj.v58i0.11730 L. Kamenski and W. Huang. How A nonconvergent recovered Hessian works in mesh adaptation. SIAM J. Numer. Anal. 52.4 (2014), pp. 1692–1708. url: http://www.jstor.org/stable/24512164
M. Krízek and P. Neittaanmäki. Superconvergence phenomenon in the finite element method arising from averaging gradients. Numer. Math. 45 (1984), pp. 105–116. doi: 10.1007/BF01379664
B. P. Lamichhane and J. Shaw-Carmody. A gradient recovery approach for nonconforming finite element methods with boundary modification. Proceedings of the 19th Biennial Computational Techniques and Applications Conference, CTAC-2020. Ed. by
W. McLean, S. Macnamara, and J. Bunder. Vol. 62. ANZIAM J. Feb. 2022, pp. C163–C175. doi: 10.21914/anziamj.v62.16032
A. Naga and Z. Zhang. A posteriori error estimates based on the polynomial preserving recovery. SIAM J. Numer. Anal. 42.4 (2004), pp. 1780–1800. doi: 10.1137/S0036142903413002
Z. Zhang and A. Naga. A new finite element gradient recovery method: Superconvergence property. SIAM J. Sci. Comput. 26.4 (2005), pp. 1192–1213. doi: 10.1137/S1064827503402837
O. C. Zienkiewicz and J. Z. Zhu. The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique. Int. J. Numer. Meth. Eng. 33 (1992), pp. 1331–1364. doi: 10.1002/nme.162033070
Tangent-filling plane curves over finite fields
No full texthttp://dx.doi.org/10.1017/S000497271200033