8 citations · 8 across the 3 of their papers we have counts for
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Behaviour of the Serre Equations in the Presence of Steep Gradients Revisited
Jordan Pitt, Christopher Zoppou, Stephen Roberts
We use numerical methods to study the behaviour of the Serre equations in the presence of steep gradients because there are no known analytical solutions for these problems. In kee…
Third-order Finite Volume/Finite Element Solution of the Fully Nonlinear Weakly Dispersive Serre Equations
Christopher Zoppou, Jordan Pitt, Stephen G. Roberts
The nonlinear weakly dispersive Serre equations contain higher-order dispersive terms. This includes a mixed derivative flux term which is difficult to handle numerically. The mix…
Local and Dimension Adaptive Sparse Grid Interpolation and Quadrature
John D. Jakeman, Stephen G. Roberts
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algo…