Bathymetry Reconstruction Using Inverse ShallowWater Models: Finite Element Discretization and Regularization

  • Hennes Hajduk
  • Dmitri KuzminEmail author
  • Vadym Aizinger
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 132)


In the present paper, we use modified shallow water equations (SWE) to reconstruct the bottom topography (also called bathymetry) of a flow domain without resorting to traditional inverse modeling techniques such as adjoint methods. The discretization in space is performed using a piecewise linear discontinuous Galerkin (DG) approximation of the free surface elevation and (linear) continuous finite elements for the bathymetry. Our approach guarantees compatibility of the discrete forward and inverse problems: for a given DG solution of the forward SWE problem, the underlying continuous bathymetry can be recovered exactly. To ensure well-posedness of the modified SWE and reduce sensitivity of the results to noisy data, a regularization term is added to the equation for the water height. A numerical study is performed to demonstrate the ability of the proposed method to recover bathymetry in a robust and accurate manner.


Bathymetry reconstruction Shallow water equations Continuous/discontinuous Galerkin method Inverse problem 



This research was supported by the German Research Association (DFG) under grant AI 117/2-1 (KU 1530/12-1).


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Authors and Affiliations

  1. 1.TU Dortmund University, Institute of Applied Mathematics (LS III)DortmundGermany
  2. 2.Chair of Scientific ComputingUniversity of BayreuthBayreuthGermany

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