Geodesic
Lakes and rivers in the landscape: A quasi-variational inequality approach
John W. Barrett1 ; Leonid Prigozhin2
1Imperial College London, United Kingdom
2Ben Gurion University of the Negev, Beer-Sheba, Israel
Interfaces and free boundaries, Tome 16 (2014) no. 2, pp. 269-296

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DOI

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.
DOI : 10.4171/ifb/320
Classification : 35-XX, 65-XX, 86-XX
Mots-clés : Quasi-variational inequality, primal and mixed formulations, numerical approximation, augmented Lagrangian method, digital elevation model, river networks

John W. Barrett  1   ; Leonid Prigozhin  2

1 Imperial College London, United Kingdom
2 Ben Gurion University of the Negev, Beer-Sheba, Israel 
John W. Barrett; Leonid Prigozhin. Lakes and rivers in the landscape: A quasi-variational inequality approach. Interfaces and free boundaries, Tome 16 (2014) no. 2, pp. 269-296. doi: 10.4171/ifb/320
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     year = {2014},
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