An hp-adaptive discontinuous Galerkin method for shallow water flows
Artikel i vetenskaplig tidskrift, 2011

An adaptive spectral/hp discontinuous Galerkin method for the two-dimensional shallow water equations is presented. The model uses an orthogonal modal basis of arbitrary polynomial order p defined on unstructured, possibly non-conforming, triangular elements for the spatial discretization. Based on a simple error indicator constructed by the solutions of approximation order p and p−1, we allow both for the mesh size, h, and polynomial approximation order to dynamically change during the simulation. For the h-type refinement, the parent element is subdivided into four similar sibling elements. The time-stepping is performed using a third-order Runge–Kutta scheme. The performance of the hp-adaptivity is illustrated for several test cases. It is found that for the case of smooth flows, p-adaptivity is more efficient than h-adaptivity with respect to degrees of freedom and computational time.

discontinuous Galerkin method



non-conforming elements

shallow water equations


Claes Eskilsson


International Journal for Numerical Methods in Fluids

0271-2091 (ISSN) 1097-0363 (eISSN)

Vol. 67 1605-1623


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