Various aglogrithms of least-squares finite-element methods (LSFEM) for convection-diffusion equation (CDE) and shallow-water equations (SWE) are formulated. The associated condition number of the resulting system of equations is systematically compared. It is found that condition number of the resulting system of equations depends on the choice of variables, interpolations, and size of element (∆x). In general, a better conditioned system is obtained by introducing auxiliary variable with low-order interpolation. The developed better conditioned shallow-water model is used to simulate wave propagation over a submerged bar and wave propagation past an elliptical hump. Computed results are compared with experiment data and other numerical approximation, and show good agreement.
Liang, Shin-Jye; Lan, Chiung-Yang; and Chen, Ying-Chih
"SHALLOW WATER FLOW MODELING USING SPACE-TIME LEAST-SQUARES FINITE-ELEMENT METHOD,"
Journal of Marine Science and Technology: Vol. 20:
5, Article 15.
Available at: https://jmstt.ntou.edu.tw/journal/vol20/iss5/15