Australian Mathematical Society (AustMS): E-Journals
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A differential-geometric perspective on magneto-hydrodynamic equilibria
No full texthttp://dx.doi.org/10.1017/S000497271200033
Variability regions for the th derivative of bounded analytic functions
No full texthttp://dx.doi.org/10.1017/S000497271200033
An upper bound for the generalised greatest common divisor of rational points
No full texthttp://dx.doi.org/10.1017/S000497271200033
Mathematical modelling and analysis of harmful algal bloom
No full texthttp://dx.doi.org/10.1017/S000497271200033
Robust virtual element methods for 3D stress-assisted diffusion problems
No full textThis article presents an initial exploration of stress-assisted diffusion problems in three dimensions within the framework of the Virtual Element Method. Hilbert spaces enriched with parameter-weighted norms, the extended Babuška–Brezzi–Braess theory for perturbed saddle-point problems, and Banach fixed-point theory play a crucial role in performing a robust analysis of the fully coupled non-linear system. The proposed virtual element formulations are provided with appropriate projection, interpolation, and stabilisation operators that ensures the well-posedness of the discrete problem. Numerical simulations are conducted to show the accuracy, performance, and applicability of themethod.
References
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L. Beirão da Veiga, F. Dassi, and G. Vacca. The Stokes complex for virtual elements in three dimensions. Math. Mod. Meth. Appl.Sci. 30 (2020), pp. 477–512. doi: 10.1142/S0218202520500128
L. Beirão da Veiga, D. Mora, and G. Vacca. The Stokes complex for virtual elements with application to Navier–Stokes flows. J. Sci. Comput. 81 (2019), 990–1018. doi: 10.1007/s10915-019-01049-
Further arithmetic properties of overcubic partition triples
No full texthttp://dx.doi.org/10.1017/S000497271200033