Abstract Fourier Neural Operators (FNOs) have proven to be an efficient and effective
method for resolution-independent operator learning in a broad variety of application areas …

The spectral/hp element method combines the geometric flexibility of the classical h-type
finite element technique with the desirable numerical properties of spectral methods …

In this paper we will review a recent emerging paradigm shift in the construction and
analysis of high order Discontinuous Galerkin methods applied to approximate solutions of …

Tsunami modeling and simulation has changed in the past few years more than it has in
decades, especially with respect to coastal inundation. Among other things, this change is …

The spatial distribution of the world population is uneven, with a density of about 40% living
in coastal regions. The trend is expected to continue in both demographic indicators and …

We extend the entropy stable high order nodal discontinuous Galerkin spectral element
approximation for the non-linear two dimensional shallow water equations presented by …

A high-order explicit finite difference scheme is derived solving the shallow water equations.
The boundary closures are based on the diagonal-norm summation-by-parts (SBP) …

In this paper, we develop, analyze and numerically test an invariant-preserving three-level
linearized implicit difference scheme for a rotation-two-component Camassa--Holm system …

Hydrodynamic modeling for coastal flooding risk assessment is a highly relevant topic. Many
operational tools available for this purpose use numerical techniques and implementation …

Discontinuous Galerkin (DG) methods have a long history in computational physics and
engineering to approximate solutions of partial differential equations due to their high-order …