Abstract
Finite element approaches generally do not guarantee exact satisfaction of conservation laws especially when Dirichlet-type boundary conditions are imposed. This article discusses improvement of the global mass conservation property of quasi-bubble finite element solutions for the shallow water equations, focusing on implementations of the surface-elevation boundary conditions. We propose two alternative implementations, which are shown by numerical verification to be effective in improving the smoothness of solutions near the boundary and in reducing the mass conservation error. The improvement of the mass conservation property contributes to augmenting the reliability and robustness of long-term time integrations. Copyright © 2006 John Wiley & Sons, Ltd.
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