- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:04
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
16
2014
2
Lakes and rivers in the landscape: A quasi-variational inequality approach
John
Barrett
Imperial College London, LONDON, UNITED KINGDOM
Leonid
Prigozhin
Ben Gurion University of the Negev, BEER-SHEBA, ISRAEL
Quasi-variational inequality, primal and mixed formulations, numerical approximation, augmented Lagrangian method, digital elevation model, river networks
We consider an evolutionary quasi-variational inequality arising in a simplified model of a network of lakes and rivers forming upon a given relief of the Earth.We regularize this model and derive its finite element approximation, in which the water flow is confined to the mesh edges. The primal and mixed formulations of the discretized quasi-variational inequality are used in the numerical simulations. The corresponding steady state problems are also analyzed. Finally, we compare this approach to the lattice algorithms employed in geographic information systems for the automatic extraction of river networks from digital elevation data, and derive similar algorithms for our approximation.
Partial differential equations
Numerical analysis
Geophysics
269
296
10.4171/IFB/320
http://www.ems-ph.org/doi/10.4171/IFB/320